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 A384249 #10 May 24 2025 00:21:55
%S A384249 1,2,3,3,5,6,7,6,8,10,11,9,13,14,15,15,17,16,19,15,21,22,23,18,24,26,
%T A384249 24,21,29,30,31,30,33,34,35,24,37,38,39,30,41,42,43,33,40,46,47,45,48,
%U A384249 48,51,39,53,48,55,42,57,58,59,45,61,62,56,48,65,66,67,51
%N A384249 The number of integers k from 1 to n such that the greatest divisor of k that is an infinitary divisor of n is squarefree.
%H A384249 Amiram Eldar, <a href="/A384249/b384249.txt">Table of n, a(n) for n = 1..10000</a>
%F A384249 Multiplicative with a(p) = p, and a(p^e) = p^e * (1 - 1/p^A065176(e)) for e >= 2.
%F A384249 Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = Product_{p prime} f(1/p) = 0.93444998595445071889..., and f(x) = 1 - (1-x^2) * Sum_{k>=2} x^(2^k)/(1-x^(2^k));
%t A384249 f[p_, e_] := p^e*(1 - 1/p^(2^IntegerExponent[e - Mod[e, 2], 2])); f[p_, 1] := p; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
%o A384249 (PARI) a(n) = {my(f = factor(n)); n * prod(i = 1, #f~, if(f[i,2] == 1, 1, 1 - 1/f[i,1]^(1 << valuation(f[i,2] - f[i,2]%2, 2))));}
%Y A384249 Cf. A005117, A065176, A077609.
%Y A384249 Analogous sequences: A063659, A384048.
%Y A384249 The number of integers k from 1 to n such that the greatest divisor of k that is an infinitary divisor of n is: A384247(1), this sequence (squarefree), A384250 (powerful), A384251 (odd), A384252 (power of 2).
%K A384249 nonn,easy,mult
%O A384249 1,2
%A A384249 _Amiram Eldar_, May 23 2025