A324984 a(n) = numerator 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, 5, 7, 59, 11, 65, 15, 743, 199, 145, 23, 5735, 27, 257, 287, 130553, 35, 24497, 39, 25159, 525, 577, 47, 2352899, 1091, 785, 11467, 67847, 59, 811525, 63, 5470699, 1217, 1297, 1355, 17310353, 75, 1601, 1671, 2005387, 83, 3114407, 87, 259879, 368879, 2305

Offset

1,2

Comments

Sum_{d|n} (pod(d)/sigma(d)) for n >= 1: 1, 5/3, 7/4, 59/21, 11/6, 65/12, 15/8, 743/105, ...

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

a(p) = 2p + 1 for p = primes (A000040).

Links

Table of n, a(n) for n=1..46.

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) = 59.

Mathematica

Array[Numerator@ DivisorSum[#, Apply[Times, Divisors@ #]/DivisorSigma[1, #] &] &, 46] (* Michael De Vlieger, Mar 24 2019 *)

Prog

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

Crossrefs

Cf. A000203, A007955, A324985 (denominators).

Sequence in context: A284380 A082714 A300090 * A106112 A260831 A268433

Adjacent sequences: A324981 A324982 A324983 * A324985 A324986 A324987

Keyword

nonn,frac

Author

Jaroslav Krizek, Mar 22 2019

Status

approved