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 A384252 #15 May 24 2025 00:21:37
%S A384252 1,2,2,4,4,4,6,8,8,8,10,8,12,12,8,16,16,16,18,16,12,20,22,16,24,24,18,
%T A384252 24,28,16,30,32,20,32,24,32,36,36,24,32,40,24,42,40,32,44,46,32,48,48,
%U A384252 32,48,52,36,40,48,36,56,58,32,60,60,48,64,48,40,66,64,44
%N A384252 The number of integers k from 1 to n such that the greatest divisor of k that is an infinitary divisor of n is a power of 2.
%H A384252 Amiram Eldar, <a href="/A384252/b384252.txt">Table of n, a(n) for n = 1..10000</a>
%F A384252 Multiplicative with a(2^e) = 2^e, and a(p^e) = p^e * (1 - 1/p^A006519(e)) if p is an odd prime.
%F A384252 a(n) = A384247(n)/A384251(n).
%F A384252 Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = Product_{p prime >= 3} f(1/p) = 0.83603370570658499764..., and f(x) = 1 - (1-x)*Sum_{k>=1} x^(2^k)/(1-x^(2^k)).
%t A384252 f[p_, e_] := p^e*(1 - 1/p^(2^(IntegerExponent[e, 2]))); f[2, e_] := 2^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]
%o A384252 (PARI) a(n) = {my(f = factor(n)); n * prod(i = 1, #f~, if(f[i,1] == 2, 1, (1 - 1/f[i,1]^(1 << valuation(f[i,2], 2)))));}
%Y A384252 Cf. A000079, A006519, A077609.
%Y A384252 Analogous sequences: A062570, A384056.
%Y A384252 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), A384249 (squarefree), A384250 (powerful), A384251 (odd), this sequence (power of 2).
%K A384252 nonn,easy,mult
%O A384252 1,2
%A A384252 _Amiram Eldar_, May 23 2025