A369911 - OEIS

%I #8 Jan 23 2025 20:30:19

%S 0,0,0,4,0,12,0,4,9,20,0,16,0,28,30,4,0,21,0,24,42,44,0,16,25,52,9,32,

%T 0,62,0,4,66,68,70,25,0,76,78,24,0,82,0,48,39,92,0,16,49,45,102,56,0,

%U 21,110,32,114,116,0,66,0,124,51,4,130,122,0,72,138,118,0,25

%N a(n) = Sum_{p|n, p prime} p * sopf(n/p).

%H Antti Karttunen, <a href="/A369911/b369911.txt">Table of n, a(n) for n = 1..20000</a>

%t a[n_] := Sum[p, {p, Select[Divisors[n], PrimeQ]}]; Table[DivisorSum[n, #*a[n/#] &, PrimeQ[#] &], {n, 100}]

%o (PARI)

%o A008472(n) = vecsum(factor(n)[, 1]);

%o A369911(n) = if(1==n, 0, my(f=factor(n)); sum(i=1, #f~, f[i,1]*A008472(n/f[i, 1]))); \\ _Antti Karttunen_, Jan 23 2025

%Y Cf. A008472 (sopf), A369744.

%K nonn,easy

%O 1,4

%A _Wesley Ivan Hurt_, Feb 05 2024