A322079 - OEIS

A322079

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

0, 1, 1, 8, 1, 13, 1, 48, 18, 29, 1, 88, 1, 53, 34, 256, 1, 153, 1, 216, 58, 125, 1, 496, 50, 173, 243, 408, 1, 361, 1, 1280, 130, 293, 74, 936, 1, 365, 178, 1264, 1, 673, 1, 984, 531, 533, 1, 2560, 98, 825, 298, 1368, 1, 1701, 146, 2416, 370, 845, 1, 2344, 1

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OFFSET

1,4

COMMENTS

Generalized formula is f(n,m) = n^m * Sum_{p^k|n} k/p^m, where f(n,0) = A001222(n) and f(n,1) = A003415(n).

LINKS

Table of n, a(n) for n=1..61.

EXAMPLE

a(40) = 1264 because 40 = 2^3 * 5, so we have 40^2 * (3/2^2 + 1/5^2) = 1264.

MATHEMATICA

f[p_, e_] := e/p^2; a[n_] := If[n==1, 0, n^2*Plus@@f@@@FactorInteger[n]]; Array[a, 60] (* Amiram Eldar, Nov 26 2018 *)

PROG