A322656 Denominator of (Sum_{d|n} sigma(d)) / sigma(n).

1, 3, 4, 7, 6, 3, 8, 15, 13, 9, 12, 28, 14, 2, 24, 31, 18, 13, 20, 6, 32, 9, 24, 6, 31, 7, 20, 56, 30, 18, 32, 21, 48, 27, 16, 91, 38, 5, 56, 45, 42, 8, 44, 84, 13, 18, 48, 124, 19, 93, 72, 98, 54, 15, 72, 20, 16, 45, 60, 24, 62, 8, 52, 127, 4, 36, 68, 126, 96

Offset: 1

Author

Jaroslav Krizek, Dec 22 2018

Keywords

• nonn
• frac

Comments

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

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

Examples

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

Links

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

Crossrefs

Cf. A000203, A007429, A319296, A221219, A322655 (numerator).

Programs

Magma

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

Mathematica

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

PARI

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

Formula

a(n) = 1 for numbers in A221219.

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