cp's OEIS Frontend

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.

A356005 Number of integers k such that k*tau(k) <= n.

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%I A356005 #20 Jul 23 2022 09:58:15
%S A356005 1,1,1,2,2,3,3,3,3,4,4,5,5,6,6,6,6,6,6,6,6,7,7,8,8,9,10,10,10,10,10,
%T A356005 11,11,12,12,12,12,13,13,14,14,14,14,14,14,15,15,15,15,15,15,15,15,15,
%U A356005 15,16,16,17,17,18,18,19,19,19,19,19,19,19,19,19,19,20,20,21,22,22,22,22,22
%N A356005 Number of integers k such that k*tau(k) <= n.
%C A356005 Partial sums of A327166. - _Rémy Sigrist_, Jul 23 2022
%H A356005 R. Balasubramanian and K. Ramachandra, <a href="https://eudml.org/doc/206090">On the number of integers n such that nd(n)<=x</a>, Acta Arith., 49 (1988), 313-322.
%H A356005 Vaclav Kotesovec, <a href="/A356005/a356005.jpg">Plot of a(n) / (n/sqrt(log(n))) for n = 1..10^7</a>
%F A356005 a(n) is asymptotic to C*n/sqrt(log(n)) for a suitable constant C > 0.
%t A356005 Table[Sum[If[k*DivisorSigma[0, k] <= n, 1, 0], {k, 1, n}], {n, 1, 100}] (* _Vaclav Kotesovec_, Jul 23 2022 *)
%o A356005 (PARI) a(n)=sum(k=1,n,if(k*numdiv(k)<=n,1,0))
%Y A356005 Cf. A038040, A327166.
%K A356005 nonn
%O A356005 1,4
%A A356005 _Benoit Cloitre_, Jul 22 2022