A324501 a(n) = numerator of Sum_{d|n} (1/pod(d)) where pod(k) = the product of the divisors of k (A007955).

1, 3, 4, 13, 6, 67, 8, 105, 37, 171, 12, 3433, 14, 323, 346, 1681, 18, 11071, 20, 14681, 652, 771, 24, 664321, 151, 1067, 1000, 38921, 30, 1681201, 32, 53793, 1552, 1803, 1646, 20396233, 38, 2243, 2146, 4737921, 42, 6258673, 44, 146345, 143506, 3267, 48

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..47.

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) = 13.

Mathematica

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

Prog

(Magma) [Numerator(&+[1 / &*[c: c in Divisors(d)]: d in Divisors(n)]): n in [1..50]]
(PARI) a(n) = numerator(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() ).numerator() for n in (1..50)] # G. C. Greubel, Mar 04 2019

Crossrefs

Cf. A007955, A324502 (denominators).

Sequence in context: A220847 A127611 A308688 * A359112 A342675 A330158

Adjacent sequences: A324498 A324499 A324500 * A324502 A324503 A324504

Keyword

nonn,frac

Author

Jaroslav Krizek, Mar 02 2019

Status

approved