A098987 Numerators in series expansion of log(Product_{m>=0} (1+q^m)).

0, 1, 1, 4, 1, 6, 2, 8, 1, 13, 3, 12, 1, 14, 4, 8, 1, 18, 13, 20, 3, 32, 6, 24, 1, 31, 7, 40, 2, 30, 4, 32, 1, 16, 9, 48, 13, 38, 10, 56, 3, 42, 16, 44, 3, 26, 12, 48, 1, 57, 31, 24, 7, 54, 20, 72, 1, 80, 15, 60, 2, 62, 16, 104, 1, 84, 8, 68, 9, 32, 24, 72, 13, 74, 19, 124, 5, 96, 28, 80, 3, 121, 21, 84, 8, 108

Offset

0,4

Links

Antti Karttunen, Table of n, a(n) for n = 0..16384

Formula

Numerators of a(n) = Sum_{d|n} ((-1)^(d+1))/d. - Ridouane Oudra, Apr 28 2019

Numerators of coefficients in expansion of Sum_{k>=1} (-1)^(k+1) * x^k / (k * (1 - x^k)). - Ilya Gutkovskiy, Oct 03 2022

Example

q + (1/2)*q^2 + (4/3)*q^3 + (1/4)*q^4 + (6/5)*q^5 + (2/3)*q^6 + (8/7)*q^7 + (1/8)*q^8 + (13/9)*q^9 + ...

Prog

(PARI) A098987(n) = if(0==n, 0, numerator(sumdiv(n, d, ((-1)^(d+1))/d))); \\ Antti Karttunen, May 06 2022

Crossrefs

Cf. A098988 (denominators).

Cf. A069519 (apparently the positions of 1's), A353687.

Sequence in context: A255198 A202521 A247362 * A174390 A153017 A038457

Adjacent sequences: A098984 A098985 A098986 * A098988 A098989 A098990

Keyword

nonn,frac

Author

N. J. A. Sloane, Oct 24 2004

Extensions

Data section extended up to term a(85) by Antti Karttunen, May 06 2022

Status

approved