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 A384420 #7 May 28 2025 10:52:04
%S A384420 0,1,1,2,1,2,1,3,2,2,1,3,1,2,2,3,1,3,1,3,2,2,1,4,2,2,3,3,1,3,1,5,2,2,
%T A384420 2,4,1,2,2,4,1,3,1,3,3,2,1,4,2,3,2,3,1,4,2,4,2,2,1,4,1,2,3,6,2,3,1,3,
%U A384420 2,3,1,5,1,2,3,3,2,3,1,4,3,2,1,4,2,2,2
%N A384420 The number of exponentially squarefree prime powers (not including 1) that divide n.
%C A384420 The number of terms in A384419 that are larger than 1 and divide n.
%H A384420 Amiram Eldar, <a href="/A384420/b384420.txt">Table of n, a(n) for n = 1..10000</a>
%F A384420 Additive with a(p^e) = A070321(e).
%F A384420 Sum_{k=1..n} a(k) ~ n*(log(log(n)) + B + C), where B is Mertens's constant (A077761), and C = Sum_{p prime, e>=2} A378085(e-1)/p^e = 0.72770645470600638249... .
%t A384420 s[n_] := Module[{k = n}, While[! SquareFreeQ[k], k--]; k]; f[p_, e_] := s[e]; a[1] = 0; a[n_] := Plus @@ f @@@ FactorInteger[n]; Array[a, 100]
%o A384420 (PARI) s(n) = while(!issquarefree(n), n--); n;
%o A384420 a(n) = vecsum(apply(s, factor(n)[, 2]));
%Y A384420 Cf. A070321, A077761, A378085, A384419, A384421.
%K A384420 nonn,easy
%O A384420 1,4
%A A384420 _Amiram Eldar_, May 28 2025