A324504 a(n) = denominator of Sum_{d|n} (d/tau(d)) where tau(k) = the number of divisors of k (A000005).

1, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 4, 15, 2, 1, 2, 3, 4, 1, 2, 3, 6, 1, 4, 1, 2, 2, 2, 15, 4, 1, 4, 3, 2, 1, 4, 3, 2, 2, 2, 3, 4, 1, 2, 3, 6, 3, 4, 1, 2, 2, 4, 1, 4, 1, 2, 6, 2, 1, 4, 105, 4, 2, 2, 3, 4, 2, 2, 3, 2, 1, 12, 1, 4, 2, 2, 15, 20, 1, 2, 2, 4

Offset

1,3

Comments

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

Links

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

Formula

a(p) = 2 for odd primes p.

a(n) = 1 for numbers n in A068977.

Example

Sum_{d|n} (d/tau(d)) for n >= 1: 1, 2, 5/2, 10/3, 7/2, 5, 9/2, 16/3, 11/2, 7, 13/2, 25/3, 15/2, 9, 35/4, 128/15, ...
For n=4; Sum_{d|4} (d/tau(d)) = 1/tau(1) + 2/tau(2) + 4/tau(4) = 1/1 + 2/2 + 4/3 = 10/3; a(4) = 3.

Mathematica

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

Prog

(Magma) [Denominator(&+[d / NumberOfDivisors(d): d in Divisors(n)]): n in [1..100]]
(PARI) a(n) = denominator(sumdiv(n, d, d/numdiv(d))); \\ Michel Marcus, Mar 03 2019
(Sage) [sum(k/sigma(k, 0) for k in n.divisors()).denominator() for n in (1..100)] # G. C. Greubel, Mar 04 2019

Crossrefs

Cf. A000005, A068977, A182463, A324503 (numerators).

Sequence in context: A002175 A170823 A068073 * A032452 A084199 A277745

Adjacent sequences: A324501 A324502 A324503 * A324505 A324506 A324507

Keyword

nonn,frac

Author

Jaroslav Krizek, Mar 03 2019

Status

approved