A322655 Numerator of (Sum_{d|n} sigma(d)) / sigma(n).

1, 4, 5, 11, 7, 5, 9, 26, 18, 14, 13, 55, 15, 3, 35, 57, 19, 24, 21, 11, 45, 13, 25, 13, 38, 10, 29, 99, 31, 35, 33, 40, 65, 38, 21, 198, 39, 7, 75, 91, 43, 15, 45, 143, 21, 25, 49, 285, 22, 152, 95, 165, 55, 29, 91, 39, 21, 62, 61, 55, 63, 11, 81, 247, 5, 65

Offset: 1

Author

Jaroslav Krizek, Dec 22 2018

Keywords

• nonn
• frac

Comments

Numerator of A007429(n) / A000203(n).

Also numerator of Sum_{d|n} (sigma(d) / sigma(n)).

Examples

			For n = 4; a(4) = numerator((Sum_{d|4} sigma(d)) / sigma(4)) = numerator((1 + 3 + 7) / (1 + 2 + 4)) = numerator(11/7) = 11.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A000203, A007429, A319296, A221219, A322656 (denominator).

Programs

Magma

[Numerator(&+[SumOfDivisors(d): d in Divisors(n)] /  SumOfDivisors(n)): n in [1..1000]];

Mathematica

Table[Numerator[Sum[DivisorSigma[1, d], {d, Divisors[n]}] / DivisorSigma[1, n]], {n, 1, 100}] (* Vaclav Kotesovec, Dec 22 2018 *)

PARI

a(n) = numerator(sumdiv(n, d, sigma(d))/sigma(n)); \\ Michel Marcus, Dec 22 2018

Formula

a(n) = A007429(n) / gcd(A000203(n), A007429(n)). - Antti Karttunen, Nov 15 2021