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.
%I A386438 #9 Jul 21 2025 11:41:33
%S A386438 1,3,4,6,6,9,8,12,11,13,12,20,14,17,18,24,18,26,20,30,24,25,24,42,27,
%T A386438 29,32,40,30,44,32,48,36,37,38,63,38,41,42,64,42,58,44,60,56,49,48,86,
%U A386438 51,60,54,70,54,77,58,86,60,61,60,109,62,65,76,96,68,86,68,90,72,88,72,137,74,77,86,100,80,100,80,132,95,85,84,145,88,89,90,130,90,144
%N A386438 a(n) = sigma(n) + omega(n) - n * Sum_{p|n, p prime} 1 / p.
%C A386438 For each divisor d of n, add 1 if n/d is prime, else add d.
%F A386438 a(n) = Sum_{d|n} d^c(n/d), where c = A005171.
%F A386438 a(n) = Sum_{d|n} (d + c(d) - phi(d)*omega(n/d)), where c = A010051.
%F A386438 a(n) = A000203(n) + A001221(n) - A069359(n).
%F A386438 a(n) = A007503(n) - A348219(n).
%t A386438 Table[Sum[d^(1 - PrimePi[n/d] + PrimePi[n/d - 1]), {d, Divisors[n]}], {n, 100}]
%Y A386438 Cf. A000010 (phi), A000203 (sigma), A001221 (omega), A005171, A007503, A010051, A069359, A348219.
%K A386438 nonn
%O A386438 1,2
%A A386438 _Wesley Ivan Hurt_, Jul 21 2025