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 A380441 #23 Aug 31 2025 15:40:06
%S A380441 1,2,2,6,2,9,2,14,11,13,2,25,2,17,18,30,2,36,2,37,24,25,2,57,27,29,38,
%T A380441 49,2,65,2,62,36,37,38,88,2,41,42,85,2,87,2,73,72,49,2,121,51,88,54,
%U A380441 85,2,117,58,113,60,61,2,161,2,65,96,126,68,131,2,109,72,133,2,192,2,77,118,121,80,153,2,181,119,85,2,215,88,89,90,169,2,227,94,145,96
%N A380441 Sum of the nonprimes dividing n and the number of distinct primes dividing n.
%C A380441 Inverse Möbius transform of A005451(n).
%C A380441 For each divisor d of n, add 1 if d is prime, else add d.
%F A380441 a(n) = sigma(n) - sopf(n) + omega(n).
%F A380441 a(n) = Sum_{d|n} d^c(d), where c = A005171.
%F A380441 a(n) = Sum_{d|n} A005451(d).
%F A380441 a(p^k) = 1 - p + (p^(k+1)-1)/(p-1) for p prime, k >= 1. - _Wesley Ivan Hurt_, Jul 02 2025
%F A380441 a(n) = A023890(n) + A001221(n). - _Wesley Ivan Hurt_, Aug 31 2025
%t A380441 Table[DivisorSigma[1, n] - Sum[p, {p, Select[Divisors[n], PrimeQ]}] + PrimeNu[n], {n, 100}]
%Y A380441 Cf. A000203 (sigma), A001221 (omega), A005171 (char nonprimes), A005451, A008472 (sopf), A023890.
%K A380441 nonn,easy,changed
%O A380441 1,2
%A A380441 _Wesley Ivan Hurt_, Jun 21 2025