but it is a little startling. With etq[q] := q^(1/24) (q;q)_∞,
In[532]:=Integrate[eta[q^4]^8/eta[q^2]^4, q]/q
In[533]:= Series[%,{q,0,105}]
Out[533]= q/2+q^3+q^5+q^7+(13 q^9)/10+q^11+q^13+(3
q^15)/2+q^17+q^19+(16 q^21)/11+q^23+(31 q^25)/26+(10
q^27)/7+q^29+q^31+(24 q^33)/17+(4 q^35)/3+q^37+(7
q^39)/5+q^41+q^43+(39 q^45)/23+q^47+(57 q^49)/50+(18 q^51)/13+q^53+(9
q^55)/7+(40 q^57)/29+q^59+q^61+(13 q^63)/8+(14 q^65)/11+q^67+(48
q^69)/35+q^71+q^73+(31 q^75)/19+(16 q^77)/13+q^79+(121
q^81)/82+q^83+(54 q^85)/43+(15 q^87)/11+q^89+(28 q^91)/23+(64
q^93)/47+(5 q^95)/4+q^97+(39 q^99)/25+q^101+q^103+(96
q^105)/53+O[q]^(1261/12)
I.e., the coeff of q^n is 1 iff n is an odd prime.
--rwg
No, Fred, that word is "bulbitated".
