A286529 - OEIS

%I #15 Jul 08 2020 05:10:26

%S 2,3,2,2,2,4,3,6,6,4,2,6,4,6,2,4,2,8,4,4,3,4,3,6,6,8,2,4,2,4,4,4,2,4,

%T 4,6,4,8,2,10,2,6,6,6,4,6,3,4,6,8,4,4,4,4,2,7,2,4,2,12,6,8,4,2,4,4,4,

%U 4,2,8,2,12,6,8,5,4,5,4,5,12,4,4,4,12,2,12,4,12,4,8,4,6,2,6,6,12,6,8,8,2,2,8,8,10,2,8,2,16,4,4,4,4,4,4,4,4,4

%N a(n) = d(n+d(n)), where d(n) is the number of divisors of n (A000005).

%H Antti Karttunen, <a href="/A286529/b286529.txt">Table of n, a(n) for n = 1..10000</a>

%H Aleksandar Ivić, <a href="https://www.jstor.org/stable/43666434">An asymptotic formula involving the enumerating function of finite Abelian groups</a>, Publikacije Elektrotehničkog fakulteta, Serija Matematika 3 (1992), pp. 61-66.

%H Imre Kátai, <a href="http://mathematica-pannonica.ttk.pte.hu/index_elemei/mp18-1/MP18-1(2007)pp11-18.pdf">On a problem of A. Ivic</a>, Mathematica Pannonica, Vol. 18, No. 1 (2007), pp. 11-18.

%F a(n) = A000005(A062249(n)) = A000005(n+A000005(n)).

%F Sum_{k=1..n} a(k) ~ D*n*log(n) + O(n*log(n)/log(log(n))), where D > 0 is a constant (conjectured with an error O(n) by Ivić, 1992; proven by Kátai, 2007). - _Amiram Eldar_, Jul 08 2020

%t Table[DivisorSigma[0, n + DivisorSigma[0, n]], {n, 117}] (* _Michael De Vlieger_, May 21 2017 *)

%o (PARI) A286529(n) = numdiv(n+numdiv(n));

%o (Scheme) (define (A286529 n) (A000005 (+ n (A000005 n))))

%o (Python)

%o from sympy import divisor_count as d

%o def a(n): return d(n + d(n)) # _Indranil Ghosh_, May 21 2017

%Y Cf. A000005, A062249, A175304, A286479, A286530.

%K nonn

%O 1,1

%A _Antti Karttunen_, May 21 2017