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 A384251 #14 May 24 2025 00:21:48
%S A384251 1,1,3,3,5,3,7,4,9,5,11,9,13,7,15,15,17,9,19,15,21,11,23,12,25,13,27,
%T A384251 21,29,15,31,16,33,17,35,27,37,19,39,20,41,21,43,33,45,23,47,45,49,25,
%U A384251 51,39,53,27,55,28,57,29,59,45,61,31,63,48,65,33,67,51,69
%N A384251 The number of integers k from 1 to n such that the greatest divisor of k that is an infinitary divisor of n is odd.
%H A384251 Amiram Eldar, <a href="/A384251/b384251.txt">Table of n, a(n) for n = 1..10000</a>
%F A384251 Multiplicative with a(2^e) = 2^e * (1 - 1/2^A006519(e)), and a(p^e) = p^e if p is an odd prime.
%F A384251 a(n) = A384247(n)/A384252(n).
%F A384251 Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = (3 - A048649)/2 = 0.79803158605891083971... .
%t A384251 a[n_] := n * If[OddQ[n], 1, 1 - 1/2^(2^(IntegerExponent[IntegerExponent[n, 2], 2]))]; Array[a, 100]
%o A384251 (PARI) a(n) = n * if(n%2, 1, (1 - 1/(1 << (1 << valuation(valuation(n, 2), 2)))));
%Y A384251 Cf. A006519, A048649, A077609.
%Y A384251 Analogous sequences: A026741, A384055.
%Y A384251 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), this sequence (odd), A384252 (power of 2).
%K A384251 nonn,easy,mult
%O A384251 1,3
%A A384251 _Amiram Eldar_, May 23 2025