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 A380457 #22 Aug 31 2025 15:34:03
%S A380457 1,4,5,8,7,14,9,16,14,20,13,30,15,26,26,32,19,41,21,44,34,38,25,62,32,
%T A380457 44,41,58,31,75,33,64,50,56,50,93,39,62,58,92,43,99,45,86,80,74,49,
%U A380457 126,58,95,74,100,55,122,74,122,82,92,61,171,63,98,106,128,86,147,69,128,98,147,73,197,75,116,126,142,98,171,81,188,122,128,85,227,110,134,122
%N A380457 Sum of divisors of n plus the number of distinct prime divisors of n: a(n) = sigma(n) + omega(n).
%C A380457 Inverse Möbius transform of A014683(n).
%C A380457 For each divisor d of n, add d+1 if d is prime, else add d.
%F A380457 a(n) = Sum_{d|n} A014683(d).
%F A380457 a(p^k) = (p^(k+1)+p-2)/(p-1) for p prime, k>=1. - _Wesley Ivan Hurt_, Jul 02 2025
%e A380457 a(12) = 1 + (2+1) + (3+1) + 4 + 6 + 12 = 30.
%t A380457 Table[DivisorSigma[1, n] + PrimeNu[n], {n, 100}]
%Y A380457 Cf. A000203 (sigma), A001221 (omega), A014683.
%K A380457 nonn,easy,changed
%O A380457 1,2
%A A380457 _Wesley Ivan Hurt_, Jun 22 2025