A225700 - OEIS

%I #11 Jan 13 2014 09:34:11

%S 2,1,1,1,10,1,1,2,1,1,11,1,26,7,1,1,17,3,1,5,1,1,23,1,50,13,1,7,29,1,

%T 1,8,11,1,35,1,1,19,13,1,82,1,43,11,1,23,47,4,1,25,1,1,53

%N Denominators of coefficients arising from q-expansion of Integrate[eta[q^4]^8/eta[q^2]^4, q]/q where eta is the Dedekind eta function.

%C Gosper observes that A225699/A225700 = A008438/(2,4,6,8,10,...) and hence the coefficient of q^k in the q-expansion is 1 iff k is an odd prime (see Example section below).

%C Note that, as usual in the OEIS, the q-expansion has been normalized here to avoid having every other term be zero.

%D R. W. Gosper, Posting to the Math Fun Mailing List, Jun 01 2013

%e 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 + ...

%Y Cf. A225700. See A008438 for eta[q^4]^8/eta[q^2]^4.

%K nonn,frac

%O 0,1

%A _N. J. A. Sloane_, Jun 01 2013