A324502 a(n) = denominator of Sum_{d|n} (1/pod(d)) where pod(k) = the product of the divisors of k (A007955).

1, 2, 3, 8, 5, 36, 7, 64, 27, 100, 11, 1728, 13, 196, 225, 1024, 17, 5832, 19, 8000, 441, 484, 23, 331776, 125, 676, 729, 21952, 29, 810000, 31, 32768, 1089, 1156, 1225, 10077696, 37, 1444, 1521, 2560000, 41, 3111696, 43, 85184, 91125, 2116, 47, 254803968, 343

Offset

1,2

Comments

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

Is this a duplicate of A007955? - R. J. Mathar, Mar 28 2019

Links

Table of n, a(n) for n=1..49.

Formula

a(n) = n for noncomposite numbers n (A008578).

Example

Sum_{d|n} (1/pod(d)) for n >= 1: 1, 3/2, 4/3, 13/8, 6/5, 67/36, 8/7, 105/64, 37/27, 171/100, 12/11, 3433/1728, ...
For n=4; Sum_{d|4} (1/pod(d)) = 1/pod(1) + 1/pod(2) + 1/pod(4) = (1/1) + (1/2) + (1/8) = 13/8; a(4) = 8.

Mathematica

Table[Denominator[Sum[Product[1/d , {d, Divisors[k]}], {k, Divisors[n]} ]], {n, 1, 50}] (* G. C. Greubel, Mar 04 2019 *)

Prog

(Magma) [Denominator(&+[1 / &*[c: c in Divisors(d)]: d in Divisors(n)]): n in [1..50]]
(PARI) a(n) = denominator(sumdiv(n, d, 1/vecprod(divisors(d)))); \\ Michel Marcus, Mar 03 2019
(Sage) [sum(product(1/j for j in k.divisors()) for k in n.divisors() ).denominator() for n in (1..50)] # G. C. Greubel, Mar 04 2019

Crossrefs

Cf. A007955, A324501 (numerators).

Sequence in context: A190997 A184392 A007955 * A170826 A162537 A369740

Adjacent sequences: A324499 A324500 A324501 * A324503 A324504 A324505

Keyword

nonn,frac

Author

Jaroslav Krizek, Mar 02 2019

Status

approved