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

Author

Michel Lagneau, Nov 22 2011

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Cf. A005063, A008472, A199583.

Programs

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 *)

Formula

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