The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A132004 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A132004

Expansion of (1 - phi(q^3) / phi(q) * phi(-q^2) * phi(-q^6)) / 2 in powers of q where phi() is a Ramanujan theta function.
(history; published version)

#26 by Charles R Greathouse IV at Fri Mar 12 22:24:44 EST 2021

LINKS

M. Michael Somos, <a href="/A010815/a010815.txt">Introduction to Ramanujan theta functions</a>

Discussion

Fri Mar 12

22:24

OEIS Server: https://oeis.org/edit/global/2897

#25 by N. J. A. Sloane at Wed Nov 13 21:58:47 EST 2019

LINKS

M. Somos, <a href="http://somos.crg4.comA010815/multiqa010815.htmltxt">Introduction to Ramanujan theta functions</a>

Discussion

Wed Nov 13

21:58

OEIS Server: https://oeis.org/edit/global/2832

#24 by Bruno Berselli at Fri Sep 07 03:08:21 EDT 2018

STATUS

reviewed

approved

#23 by Peter Luschny at Fri Sep 07 01:32:57 EDT 2018

STATUS

proposed

reviewed

#22 by Jianing Song at Thu Sep 06 23:58:43 EDT 2018

STATUS

editing

proposed

#21 by Jianing Song at Thu Sep 06 23:58:37 EDT 2018

FORMULA

a(n) is multiplicative with a(2^e) = 2*0^e - 1, a(3^e) = 1, a(p^e) = e + 1 if p == 1 (mod 4), a(p^e) = (1 + (-1)^e) / 2 if p == 3 (mod 4).

G.f.: Sum_{k>0} x^k / (1 + x^k) * Kronecker( -36, k).

a(3*n) = a(n). -2 * a(n) = A132003(n) unless n = 0. a(2*n) = - A035154(n). a(2*n + 1) = A125079(n).

STATUS

reviewed

editing

#20 by Wesley Ivan Hurt at Thu Sep 06 22:44:07 EDT 2018

STATUS

proposed

reviewed

#19 by Jon E. Schoenfield at Thu Sep 06 22:43:56 EDT 2018

STATUS

editing

proposed

#18 by Jon E. Schoenfield at Thu Sep 06 22:43:53 EDT 2018

FORMULA

G.f.: Sum_{k>0} x^k / (1 + x^k) * kroneckerKronecker( -36, k).

STATUS

approved

editing

#17 by Alois P. Heinz at Sun Sep 24 15:52:30 EDT 2017

STATUS

proposed

approved