A307100 a(n) = Sum_{d|n} (tau(d)*pod(d)) where tau(k) = the number of divisors of k (A000005) and pod(k) = the product of the divisors of k (A007955).

1, 5, 7, 29, 11, 155, 15, 285, 88, 415, 23, 10547, 27, 803, 917, 5405, 35, 35228, 39, 48439, 1785, 1963, 47, 2665011, 386, 2735, 3004, 132539, 59, 6481465, 63, 202013, 4385, 4663, 4925, 90744884, 75, 5819, 6117, 20528695, 83, 24896285, 87, 513091, 547748, 8515

Offset

1,2

Comments

n divides a(n) for n = 1, 21, 333592, ...

Links

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

Formula

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

Example

a(6) = tau(1)*pod(1) + tau(2)*pod(2) + tau(3)*pod(3) + tau(6)*pod(6) = (1*1) + (2*2) + (2*3) + (4*36) = 155.

Prog

(Magma) [&+[# [c: c in Divisors(d)] * &*[c: c in Divisors(d)]: d in Divisors(n)]: n in [1..100]]
(PARI) a(n) = sumdiv(n, d, my(dd=divisors(d)); #dd*vecprod(dd)); \\ Michel Marcus, Apr 25 2019

Crossrefs

Cf. A000005, A007955, A307101.

Sequence in context: A358582 A185302 A179305 * A229337 A227857 A266078

Adjacent sequences: A307097 A307098 A307099 * A307101 A307102 A307103

Keyword

nonn

Author

Jaroslav Krizek, Apr 25 2019

Status

approved