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 A380449 #26 Jul 02 2025 16:17:56
%S A380449 2,4,5,9,7,14,9,18,15,20,13,32,15,26,26,35,19,43,21,46,34,38,25,66,33,
%T A380449 44,43,60,31,77,33,68,50,56,50,98,39,62,58,96,43,101,45,88,82,74,49,
%U A380449 132,59,97,74,102,55,126,74,126,82,92,61,177,63,98,108,133,86,149,69,130,98,149,73,205,75,116,128,144,98,173,81,194,125,128,85,233,110,134,122
%N A380449 Sum of the divisors of n plus the number of nonprime divisors of n.
%C A380449 Inverse Möbius transform of A113636(n).
%C A380449 For each divisor d of n, add d if d is prime, else add d+1.
%F A380449 a(n) = sigma(n) + tau(n) - omega(n).
%F A380449 a(n) = Sum_{d|n} A113636(d).
%F A380449 a(n) = A000203(n) + A033273(n).
%F A380449 a(p^k) = k + (p^(k+1)-1)/(p-1), p prime, k >= 1. - _Wesley Ivan Hurt_, Jul 02 2025
%e A380449 The sum of the divisors of 12 = 1+2+3+4+6+12 = 28 and 12 has 4 nonprime divisors, so a(12) = 28 + 4 = 32.
%t A380449 Table[DivisorSigma[0, n] - PrimeNu[n] + DivisorSigma[1, n], {n, 100}]
%Y A380449 Cf. A000005 (tau), A000203 (sigma), A001221 (omega), A033273, A113636.
%K A380449 nonn,easy
%O A380449 1,1
%A A380449 _Wesley Ivan Hurt_, Jun 21 2025