A322664 a(n) = n^2 * Sum_{p^k|n} Sum_{j=1..k} 1/p^(2*j), where p are primes dividing n with multiplicity k.

0, 1, 1, 5, 1, 13, 1, 21, 10, 29, 1, 61, 1, 53, 34, 85, 1, 121, 1, 141, 58, 125, 1, 253, 26, 173, 91, 261, 1, 361, 1, 341, 130, 293, 74, 565, 1, 365, 178, 589, 1, 673, 1, 621, 331, 533, 1, 1021, 50, 729, 298, 861, 1, 1093, 146, 1093, 370, 845, 1, 1669, 1, 965

Offset

1,4

Comments

The generalized formula is f(n,m) = n^m * Sum_{p^k|n} Sum_{j=1..k} 1/p^(m*j), where f(n,0) = A001222(n) and f(n,1) = A095112(n).

Links

Table of n, a(n) for n=1..62.

Formula

Sum_{k=1..n} a(k) ~ A286229 * A000330(n).

Example

The prime factorization of 24 is 2^3 * 3, so a(24) = 24^2 * (1/2^2 + 1/2^(2*2) + 1/2^(2*3) + 1/3^2) = 253.

Prog

(PARI) a(n) = my(f=factor(n)); sum(k=1, #f~, sum(j=1, f[k, 2], n^2 / f[k, 1]^(2*j)));

Crossrefs

Cf. A001222, A095112, A286229.

Sequence in context: A276738 A094049 A286254 * A286457 A327766 A147348

Adjacent sequences: A322661 A322662 A322663 * A322665 A322666 A322667

Keyword

nonn

Author

Daniel Suteu, Dec 22 2018

Status

approved