A200768 Sum of the n-th powers of the distinct prime divisors of n.

0, 4, 27, 16, 3125, 793, 823543, 256, 19683, 9766649, 285311670611, 535537, 302875106592253, 678223089233, 30531927032, 65536, 827240261886336764177, 387682633, 1978419655660313589123979, 95367432689201, 558545874543637210, 81402749386839765307625

Offset

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..388

Formula

a(n) = Sum_{p|n} p^n. - Wesley Ivan Hurt, Jun 14 2021

Example

a(6) = 793 because the distinct prime divisors of 6 are 2 and 3, and 2^6 + 3^6 = 793.

Maple

f:= proc(n) local p;
   add(p^n, p = numtheory:-factorset(n))
end proc:
map(f, [$1..30]); # Robert Israel, Feb 20 2024

Mathematica

Prepend[Array[Plus@@First[Transpose[FactorInteger[#]^#]]&, 100, 2], 0]
Join[{0}, Table[Total[FactorInteger[n][[All, 1]]^n], {n, 2, 25}]] (* Harvey P. Dale, Jan 23 2021 *)

Crossrefs

Cf. A005063, A008472, A199583.

Sequence in context: A133482 A108139 A351365 * A176147 A176031 A093845

Adjacent sequences: A200765 A200766 A200767 * A200769 A200770 A200771

Keyword

nonn

Author

Michel Lagneau, Nov 22 2011

Status

approved