cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A200768 #23 Feb 21 2024 08:27:11
%S A200768 0,4,27,16,3125,793,823543,256,19683,9766649,285311670611,535537,
%T A200768 302875106592253,678223089233,30531927032,65536,827240261886336764177,
%U A200768 387682633,1978419655660313589123979,95367432689201,558545874543637210,81402749386839765307625
%N A200768 Sum of the n-th powers of the distinct prime divisors of n.
%H A200768 Robert Israel, <a href="/A200768/b200768.txt">Table of n, a(n) for n = 1..388</a>
%F A200768 a(n) = Sum_{p|n} p^n. - _Wesley Ivan Hurt_, Jun 14 2021
%e A200768 a(6) = 793 because the distinct prime divisors of 6 are 2 and 3, and 2^6 + 3^6 = 793.
%p A200768 f:= proc(n) local p;
%p A200768    add(p^n, p = numtheory:-factorset(n))
%p A200768 end proc:
%p A200768 map(f, [$1..30]); # _Robert Israel_, Feb 20 2024
%t A200768 Prepend[Array[Plus@@First[Transpose[FactorInteger[#]^#]]&,100,2],0]
%t A200768 Join[{0},Table[Total[FactorInteger[n][[All,1]]^n],{n,2,25}]] (* _Harvey P. Dale_, Jan 23 2021 *)
%Y A200768 Cf. A005063, A008472, A199583.
%K A200768 nonn
%O A200768 1,2
%A A200768 _Michel Lagneau_, Nov 22 2011