A225699 Numerators 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.

1, 1, 1, 1, 13, 1, 1, 3, 1, 1, 16, 1, 31, 10, 1, 1, 24, 4, 1, 7, 1, 1, 39, 1, 57, 18, 1, 9, 40, 1, 1, 13, 14, 1, 48, 1, 1, 31, 16, 1, 121, 1, 54, 15, 1, 28, 64, 5, 1, 39, 1, 1, 96

Offset: 0

Author

N. J. A. Sloane, Jun 01 2013

Keywords

• nonn
• frac

Comments

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).

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

Examples

			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 + ...
		

References

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

Crossrefs

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