A324985 a(n) = denominator of Sum_{d|n} (pod(d)/sigma(d)) where pod(k) = the product of the divisors of k (A007955) and sigma(k) = the sum of the divisors of k (A000203).

1, 3, 4, 21, 6, 12, 8, 105, 52, 18, 12, 84, 14, 24, 24, 3255, 18, 156, 20, 126, 32, 36, 24, 420, 186, 42, 520, 168, 30, 72, 32, 9765, 48, 54, 48, 156, 38, 60, 56, 70, 42, 96, 44, 252, 312, 72, 48, 13020, 456, 558, 72, 294, 54, 1560, 72, 840, 16, 90, 60, 504

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..60.

Example

For n=4; Sum_{d|4} (pod(d)/sigma(d)) = pod(1)/sigma(1) + pod(2)/sigma(2) + pod(4)/sigma(4) = 1/1 + 2/3 + 8/7 = 59/21;  a(4) = 21.

Mathematica

Array[Denominator@ DivisorSum[#, Apply[Times, Divisors@ #]/DivisorSigma[1, #] &] &, 60] (* Michael De Vlieger, Mar 24 2019 *)

Prog

(Magma) [Denominator(&+[&*[c: c in Divisors(d)] / SumOfDivisors(d): d in Divisors(n)]): n in [1..100]]
(PARI) a(n) = denominator(sumdiv(n, d, vecprod(divisors(d))/sigma(d))); \\ Michel Marcus, Mar 23 2019

Crossrefs

Cf. A000203, A007955, A324984 (numerators).

Sequence in context: A265710 A322673 A306650 * A069934 A206031 A206032

Adjacent sequences: A324982 A324983 A324984 * A324986 A324987 A324988

Keyword

nonn,frac

Author

Jaroslav Krizek, Mar 22 2019

Status

approved