A225700 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.

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

Offset

0,1

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.

References

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

Links

Table of n, a(n) for n=0..52.

Example

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 + ...

Crossrefs

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

Sequence in context: A208896 A288972 A065521 * A156188 A179930 A007737

Adjacent sequences: A225697 A225698 A225699 * A225701 A225702 A225703

Keyword

nonn,frac

Author

N. J. A. Sloane, Jun 01 2013

Status

approved