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A200768
Sum of the n-th powers of the distinct prime divisors of n.
4
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
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
KEYWORD
nonn
AUTHOR
Michel Lagneau, Nov 22 2011
STATUS
approved