A324510 a(n) = denominator of Product_{d|n} (sigma(d)/tau(d)) where sigma(k) = the sum of the divisors of k (A000203) and tau(k) = the number of divisors of k (A000005).

1, 2, 1, 2, 1, 1, 1, 8, 3, 4, 1, 1, 1, 1, 1, 8, 1, 2, 1, 4, 1, 1, 1, 4, 1, 4, 3, 1, 1, 1, 1, 16, 1, 4, 1, 27, 1, 1, 1, 64, 1, 1, 1, 1, 1, 1, 1, 2, 1, 8, 1, 4, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 9, 16, 1, 1, 1, 4, 1, 1, 1, 96, 1, 4, 1, 1, 1, 1, 1, 64, 3, 4, 1, 1, 1

Offset

1,2

Comments

Product_{d|n} (sigma(d)/tau(d)) >= 1 for all n >= 1.

Links

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

Formula

a(n) = 1 for numbers in A324511.

Example

Product_{d|n} (sigma(d)/tau(d)) for n >= 1: 1, 3/2, 2, 7/2, 3, 9, 4, 105/8, 26/3, 81/4, 6, 98, 7, 36, 36, 651/8, ...
For n=4; Product_{d|4} (sigma(d)/tau(d)) = sigma(1)/tau(1) + sigma(2)/tau(2) + sigma(4)/tau(4) = (1/1) * (3/2) * (7/3) = 7/2; a(4) = 2.

Mathematica

Table[Denominator[Product[DivisorSigma[1, k]/DivisorSigma[0, k], {k, Divisors[n]}]], {n, 1, 100}] (* G. C. Greubel, Mar 04 2019 *)

Prog

(Magma) [Denominator(&*[SumOfDivisors(d) / NumberOfDivisors(d): d in Divisors(n)]): n in [1..100]]
(Sage) [product(sigma(k, 1)/sigma(k, 0) for k in n.divisors() ).denominator() for n in (1..100)] # G. C. Greubel, Mar 04 2019
(PARI) A324510(n) = { my(m=1); fordiv(n, d, m *= sigma(d)/numdiv(d)); denominator(m); }; \\ Antti Karttunen, Dec 06 2021

Crossrefs

Cf. A000005, A000203, A324509 (numerators), A324511.

Sequence in context: A174110 A264969 A320301 * A061916 A351819 A076348

Adjacent sequences: A324507 A324508 A324509 * A324511 A324512 A324513

Keyword

nonn,frac

Author

Jaroslav Krizek, Mar 03 2019

Status

approved