the denominator of the sum of the first n Harmonic numbers, [[see PS below]] equals LCM(1,2,..,n) for values of n of the form n=(p-1) , p prime. Not all primes qualify for the converse statement. Those that do (listed below by prime_index PrimePi(p) 1,2,3; 5,6,7; 10,11; 16; 24,25; 31,32,33,34,35,36; ... or as {start index of patch, length of patch} {{1, 3}, {5, 3}, {10, 2}, {16, 1}, {24, 2}, {31, 6}, {54, 5}, {62, 1}, {164, 16}, {220, 12}, {358, 10}, {446, 31}, {488, 24}, {520, 31}, {887, 10}, {910, 51}, {986, 5}, {1001, 7},... Who can explain this Patchy behaviour? PS. [[ (-n+(1+n)HarmonicNumber[n]) or -n +(1+n)(EulerGamma+PolyGamma[0,n+1]) since Mma burps on HarmonicNumber[k] with k>1000. ]] Wouter. =============================== This email is confidential and intended solely for the use of the individual to whom it is addressed. If you are not the intended recipient, be advised that you have received this email in error and that any use, dissemination, forwarding, printing, or copying of this email is strictly prohibited. You are explicitly requested to notify the sender of this email that the intended recipient was not reached.