Apologies for multiple copies of this rather long message, but I'm keen to find a few potential editors for the following scheme. If you are able to help, send to me personally, not to bother the rest of the lists. I can then send you attachments of even longer files, and we can divvy up the work so that there is only enough duplication to ensure checking. Here is the preface to a file: This is a list, in OEIS numerical order, of divisibility sequences. The suggestion is that these should be given the codeword ``div'' (or ``divi'' if codewords all have four letters). Where this is not already done, it should be remarked that they are divisibility sequences. Many are values of Chebyshev polynomials: for these the polynomial should be quoted. Those which satisfy recurrence relations should include the recurrence and the generating function. A `closed' formula is also always possible. Divisibility sequences satisfying recurrence relations of order 4 or higher may contain prime divisors with more than one rank of apparition. At least the first few examples of this should be noted. Many higher order sequences factor into ones of lower order: this should be noted. Check list for div seqs in (and not yet in) OEIS: 1. Is it stated that it's a divisibility seq ? Should there be a keyword, say `divi' ? 2. Check the offset. The ``right'' offset is $a(0)=0$, but there may be a good reason for having two entries with different offsets. For example, the Fibonacci sequence would normally be given as $a(0)=0$, 1, 1, 2, 3, 5, \ldots, but it often manifests itself as $a(0)=1$, 1, 2, 3, 5, \ldots, e.g., the number of ways of packing $n$ dominoes in a $2\times n$ box. 3. If a divisibility sequence is multiplied or divided through by an integer, it remains a divisibility sequence, so, in order to be sure of locating all manifestations, if a (the) ``natural'' occurrence of the sequence has $a(1)=k$, then the division by $k$, starting $a(0)=0$, $a(1)=1$ should also be given, and often the versions with $a(1)=2$, 3, etc., up to a point, should be given as well. 4. Is there a recurrence relation ? Note that, paradoxically, there may be more than one, and of different orders, because of factorization. 5. Is the generating function given ? 6. Is there a ``closed'' formula of type $A\alpha^n+B\beta^n+C\gamma^n+\cdots$ ? 7. Does the sequence factor into recurring sequences of lower order (which are not necessarily divisibility sequences) over the integers ? over other number fields ? 8. Are the terms values of one or more Chebyshev polynomials ? 9. Note that every second term forms a divisibility sequence which may be worthy of mention in its own right. Similarly for every third term, every fourth term, \ldots . 10. Numbertheoretic properties, e.g., the rank(s) of apparition of primes, may be worthy of note. In sequences of order $2^k$ a prime may have as many as $k$ ranks of apparition. Second order linear recurrences are often numerators or denominators of convergents to continued fractions of quadratic irrationals. Many 2nd order sequences are related to solutions of Bramahgupta-Bhaskara-Pell equations 11. Cross-references to other sequences, especially those arising from 2., 3., 6., 8., \& 9.\ above. 12. Does the sequence arise ``in real life'' as the number of points on an elliptic curve; or the number of perfect matchings in a family of graphs; or the numer of spanning trees (sometimes called the `complexity') thereof, or in other ways? Note that perfect matchings are also called dimer problems or domino tilings or packings. 13. If it's a second order sequence, then I believe that $a_n=F_{rn}/s$ for some $(r,s)$, where $F_n$ is the $n$\,th Fibonacci number. If so, then $r$ and $s$ should be given. 14. Other things that I've missed. For a start, compare and contrast the descriptions of A010892, A000027, A001906, A001353, A004254, A001109, A004187, A001090, A018913, A004189, A004190, A004191, A078362, A007655, A078364, A077412, A078366, A049660, A078368, A075843, A092449, A077421, A097778, A077423, A097780, A097309, A097781, A097311, A097782, A097313, and note that the varied properties that are mentioned are in fact shared by ALL of them, though rarely are more than one or two mentioned. When, as with the above examples, a sequence belongs to a family, it would be good to give the family a name, and say which member it is. The companion sequence of sequences is A000045, A000129, A006190, A001076, A052918, A005668, A054413, A041025, A099371, A041041, A049666, A041061, A140455, A041085, A154597, A041113, missing, A041145, missing, A041181, missing, A041221, missing, A041265, missing, A041313, missing, A041365, A049667, A041421, missing, A041481, missing, A041545, missing, A041613, missing, A041685, missing, A041761, missing, A041841, missing, A041925, missing, A042013, missing, A042105, missing, A042201, missing, A042301, missing, A042405, missing, A042513, missing, A042625, missing, A042741, [perhaps itself a more interesting sequence than many that are submitted?] The major interest of divisibility sequences is the factorization of the terms. It would be good to have this, perhaps on a separate page. In this sense, all of the 'Cunningham project' should be accessible via OEIS. Thankyou for your patience, if you've got as far as this. R.