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A200768 Sum of the n-th powers of the distinct prime divisors of n. 3

%I #23 Feb 21 2024 08:27:11

%S 0,4,27,16,3125,793,823543,256,19683,9766649,285311670611,535537,

%T 302875106592253,678223089233,30531927032,65536,827240261886336764177,

%U 387682633,1978419655660313589123979,95367432689201,558545874543637210,81402749386839765307625

%N Sum of the n-th powers of the distinct prime divisors of n.

%H Robert Israel, <a href="/A200768/b200768.txt">Table of n, a(n) for n = 1..388</a>

%F a(n) = Sum_{p|n} p^n. - _Wesley Ivan Hurt_, Jun 14 2021

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

%p f:= proc(n) local p;

%p add(p^n, p = numtheory:-factorset(n))

%p end proc:

%p map(f, [$1..30]); # _Robert Israel_, Feb 20 2024

%t Prepend[Array[Plus@@First[Transpose[FactorInteger[#]^#]]&,100,2],0]

%t Join[{0},Table[Total[FactorInteger[n][[All,1]]^n],{n,2,25}]] (* _Harvey P. Dale_, Jan 23 2021 *)

%Y Cf. A005063, A008472, A199583.

%K nonn

%O 1,2

%A _Michel Lagneau_, Nov 22 2011

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Last modified March 29 06:44 EDT 2024. Contains 371265 sequences. (Running on oeis4.)