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 A384421 #8 May 28 2025 10:51:59
%S A384421 0,1,1,1,1,2,1,1,1,2,1,2,1,2,2,0,1,2,1,2,2,2,1,2,1,2,1,2,1,3,1,1,2,2,
%T A384421 2,2,1,2,2,2,1,3,1,2,2,2,1,1,1,2,2,2,1,2,2,2,2,2,1,3,1,2,2,1,2,3,1,2,
%U A384421 2,3,1,2,1,2,2,2,2,3,1,1,0,2,1,3,2,2,2
%N A384421 The number of exponentially squarefree prime powers (not including 1) that unitarily divide n.
%C A384421 First differs from A125029 at n = 64.
%C A384421 A number k unitarily divides n if k|n and gcd(k, n/k) = 1.
%C A384421 The number of unitary divisors of n that are larger than 1 and are terms in A384419.
%H A384421 Amiram Eldar, <a href="/A384421/b384421.txt">Table of n, a(n) for n = 1..10000</a>
%F A384421 Additive with a(p^e) = A008966(e).
%F A384421 Sum_{k=1..n} a(k) ~ n*(log(log(n)) + B - C + D), where B is Mertens's constant (A077761), C = Sum_{p prime} 1/p^2 (A085548), and D = Sum_{p prime, e>=2} (1-1/p)*A008966(e)/p^e = 0.40780808646244052181... .
%t A384421 f[p_, e_] := If[SquareFreeQ[e], 1, 0]; a[1] = 0; a[n_] := Plus @@ f @@@ FactorInteger[n]; Array[a, 100]
%o A384421 (PARI) a(n) = vecsum(apply(issquarefree, factor(n)[, 2]));
%Y A384421 Cf. A008966, A125029, A383959, A384419, A384420.
%K A384421 nonn,easy
%O A384421 1,6
%A A384421 _Amiram Eldar_, May 28 2025