A353688 -id:A353688 - cp's OEIS frontend

A098988 Denominators in series expansion of log(Product_{m>=1} (1+q^m)).

1, 1, 2, 3, 4, 5, 3, 7, 8, 9, 5, 11, 3, 13, 7, 5, 16, 17, 18, 19, 10, 21, 11, 23, 6, 25, 13, 27, 7, 29, 5, 31, 32, 11, 17, 35, 36, 37, 19, 39, 20, 41, 21, 43, 11, 15, 23, 47, 12, 49, 50, 17, 26, 53, 27, 55, 7, 57, 29, 59, 5, 61, 31, 63, 64, 65, 11, 67, 34, 23, 35, 71, 72, 73, 37, 75, 19, 77, 39, 79, 40, 81, 41, 83, 21

Offset: 0

N. J. A. Sloane, Oct 24 2004

			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 + ...

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

Cf. A098987 (numerators), A353688 (n / a(n)).

A098988(n) = if(0==n, 1, denominator(sumdiv(n,d, ((-1)^(d+1))/d))); \\ Antti Karttunen, May 06 2022

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

Denominators of coefficients in expansion of Sum_{k>=1} (-1)^(k+1) * x^k / (k * (1 - x^k)). - Ilya Gutkovskiy, Aug 04 2023

Data section extended up to term a(84) by Antti Karttunen, May 06 2022

A353666 a(n) = gcd(n, A351546(n)).

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 4, 1, 2, 3, 1, 1, 1, 1, 2, 1, 2, 1, 4, 1, 2, 1, 28, 1, 2, 1, 1, 3, 2, 1, 1, 1, 2, 1, 10, 1, 2, 1, 4, 3, 2, 1, 4, 1, 1, 3, 2, 1, 2, 1, 8, 1, 2, 1, 4, 1, 2, 1, 1, 1, 2, 1, 2, 3, 2, 1, 1, 1, 2, 1, 4, 1, 2, 1, 2, 1, 2, 1, 28, 1, 2, 3, 4, 1, 2, 7, 4, 1, 2, 5, 4, 1, 1, 3, 1, 1, 2, 1, 2, 3

Offset: 1

Antti Karttunen, May 04 2022

nonn

Cf. A351546, A353667, A353668.

Differs from A353688 for the first time at n = 28, 30, 40, 60, 66, 84, 90, 102, 120, ...

A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A351546(n) = { my(f=factor(sigma(n)), u=A003961(n)); prod(k=1, #f~, f[k, 1]^((0!=(u%f[k, 1]))*f[k, 2])); };
A353666(n) = gcd(n, A351546(n));

a(n) = gcd(n, A351546(n)).

a(n) = n / A353667(n) = A351546(n) / A353668(n).

cp's OEIS Frontend

A098988 Denominators in series expansion of log(Product_{m>=1} (1+q^m)).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

PARI

Formula

Extensions