A098987 - OEIS

%I #22 Oct 23 2022 23:59:27

%S 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,

%T 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,

%U 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

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

%H Antti Karttunen, <a href="/A098987/b098987.txt">Table of n, a(n) for n = 0..16384</a>

%F Numerators of a(n) = Sum_{d|n} ((-1)^(d+1))/d. - _Ridouane Oudra_, Apr 28 2019

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

%e 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 + ...

%o (PARI) A098987(n) = if(0==n, 0, numerator(sumdiv(n,d, ((-1)^(d+1))/d))); \\ _Antti Karttunen_, May 06 2022

%Y Cf. A098988 (denominators).

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

%K nonn,frac

%O 0,4

%A _N. J. A. Sloane_, Oct 24 2004

%E Data section extended up to term a(85) by _Antti Karttunen_, May 06 2022