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 A366988 #12 Nov 02 2023 10:25:11
%S A366988 0,0,0,1,0,0,0,2,1,0,0,1,0,0,0,2,0,1,0,1,0,0,0,2,1,0,2,1,0,0,0,3,0,0,
%T A366988 0,2,0,0,0,2,0,0,0,1,1,0,0,2,1,1,0,1,0,2,0,2,0,0,0,1,0,0,1,3,0,0,0,1,
%U A366988 0,0,0,3,0,0,1,1,0,0,0,2,2,0,0,1,0,0,0
%N A366988 The number of prime powers of prime numbers (A053810) that divide n.
%C A366988 a(n) depends only on the prime signature of n.
%C A366988 Every nonnegative number appears in the sequence of record values. k >= 1 first occurs at n = 2^prime(k) (A034785).
%H A366988 Amiram Eldar, <a href="/A366988/b366988.txt">Table of n, a(n) for n = 1..10000</a>
%F A366988 Additive with a(p^e) = A000720(e).
%F A366988 a(n) = 0 if and only if n is squarefree (A005117).
%F A366988 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{p prime} P(p) = 0.67167522222173297323..., where P(s) is the prime zeta function.
%t A366988 f[p_, e_] := PrimePi[e]; a[1] = 0; a[n_] := Plus @@ f @@@ FactorInteger[n]; Array[a, 100]
%o A366988 (PARI) a(n) = {my(f = factor(n)); sum(i = 1, #f~, primepi(f[i, 2]));}
%Y A366988 Cf. A000720, A005117, A034785, A053810, A095691, A366989, A366990, A366993.
%K A366988 nonn,easy
%O A366988 1,8
%A A366988 _Amiram Eldar_, Oct 31 2023