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

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

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

Crossrefs

Cf. A001222, A003415.

Sequence in context: A045771 A070488 A349142 * A124906 A298143 A181762

Adjacent sequences: A322076 A322077 A322078 * A322080 A322081 A322082

Keyword

nonn

Author

Daniel Suteu, Nov 25 2018

Status

approved