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 A380447 #27 Aug 31 2025 15:46:47
%S A380447 1,3,4,9,6,14,8,25,19,22,12,50,14,30,32,65,18,74,20,82,44,46,24,146,
%T A380447 51,54,82,114,30,153,32,161,68,70,72,254,38,78,80,242,42,213,44,178,
%U A380447 182,94,48,386,99,202,104,210,54,326,112,338,116,118,60,543,62,126,254,385,132,333,68,274,140,353,72,722,74,150,302,306,156,393,80,642,325,166
%N A380447 Number of primes dividing n plus n times the number of nonprimes dividing n.
%C A380447 For each divisor d of n, add 1 if d is prime, else add n.
%C A380447 Inverse Möbius transform of A385313(n).
%F A380447 a(n) = n*tau(n) - (n-1)*omega(n).
%F A380447 a(n) = Sum_{d|n} n^c(d), where c = A005171.
%F A380447 a(n) = Sum_{d|n} A385313(d).
%F A380447 a(p^k) = 1 + k*p^k for p prime and k>=1. - _Wesley Ivan Hurt_, Jul 02 2025
%F A380447 a(n) = A001221(n) - n*A033273(n). - _Wesley Ivan Hurt_, Aug 31 2025
%e A380447 12 has 2 prime divisors and 4 nonprime divisors, so a(12) = (2) + 12*(4) = 50.
%t A380447 Table[n*DivisorSigma[0, n] - (n - 1) PrimeNu[n], {n, 100}]
%Y A380447 Cf. A000005 (tau), A001221 (omega), A005171, A033273.
%K A380447 nonn,easy,changed
%O A380447 1,2
%A A380447 _Wesley Ivan Hurt_, Jun 21 2025