cp's OEIS Frontend

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.

A345354 a(n) = Sum_{p|n, p prime} omega(n/p).

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%I A345354 #16 Mar 18 2022 00:30:31
%S A345354 0,0,0,1,0,2,0,1,1,2,0,3,0,2,2,1,0,3,0,3,2,2,0,3,1,2,1,3,0,6,0,1,2,2,
%T A345354 2,4,0,2,2,3,0,6,0,3,3,2,0,3,1,3,2,3,0,3,2,3,2,2,0,7,0,2,3,1,2,6,0,3,
%U A345354 2,6,0,4,0,2,3,3,2,6,0,3,1,2,0,7,2,2,2,3,0,7,2,3
%N A345354 a(n) = Sum_{p|n, p prime} omega(n/p).
%F A345354 a(p) = 0 for p prime.
%F A345354 a(n) = Sum_{a*b*c=n} omega(a)*omega(b)*mu(c). - _Benedict W. J. Irwin_, Mar 02 2022
%e A345354 a(30) = Sum_{p|30} omega(30/p) = omega(15) + omega(10) + omega(6) = 2 + 2 + 2 = 6.
%t A345354 Table[Sum[PrimeNu[n/k] (PrimePi[k] - PrimePi[k - 1]) (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 100}]
%o A345354 (PARI) a(n) = my(f=factor(n)); sum(k=1, #f~, omega(n/f[k,1])); \\ _Michel Marcus_, Jun 16 2021
%Y A345354 Cf. A001221 (omega).
%K A345354 nonn
%O A345354 1,6
%A A345354 _Wesley Ivan Hurt_, Jun 15 2021