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.

A074794 Number of numbers k <= n such that tau(k) == 1 (mod 3) where tau(k) = A000005(k) is the number of divisors of k.

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%I A074794 #25 Feb 02 2025 02:12:36
%S A074794 1,1,1,1,1,2,2,3,3,4,4,4,4,5,6,6,6,6,6,6,7,8,8,8,8,9,10,10,10,10,10,
%T A074794 10,11,12,13,13,13,14,15,15,15,15,15,15,15,16,16,17,17,17,18,18,18,18,
%U A074794 19,19,20,21,21,21,21,22,22,23,24,24,24,24,25,25,25,25,25,26,26,26,27,27
%N A074794 Number of numbers k <= n such that tau(k) == 1 (mod 3) where tau(k) = A000005(k) is the number of divisors of k.
%H A074794 Amiram Eldar, <a href="/A074794/b074794.txt">Table of n, a(n) for n = 1..10000</a>
%F A074794 a(n) is asymptotic to c*n with c = 0.36....
%F A074794 The constant is conjecturally 3*zeta(3)/Pi^2 = 0.3653814847007... (A346602). See A211337 for more details. - _Amiram Eldar_, Feb 01 2025
%t A074794 Accumulate[Table[Boole[Mod[DivisorSigma[0, n], 3] == 1], {n, 1, 100}]] (* _Amiram Eldar_, Aug 29 2020 *)
%o A074794 (PARI) a(n)=sum(k=1,n,if(numdiv(k)%3-1,0,1))
%Y A074794 Cf. A000005, A074795, A074796, A211337, A346602.
%K A074794 nonn
%O A074794 1,6
%A A074794 _Benoit Cloitre_, Sep 07 2002