A286529 a(n) = d(n+d(n)), where d(n) is the number of divisors of n (A000005).

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, 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, 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

Offset: 1

Author

Antti Karttunen, May 21 2017

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Aleksandar Ivić, An asymptotic formula involving the enumerating function of finite Abelian groups, Publikacije Elektrotehničkog fakulteta, Serija Matematika 3 (1992), pp. 61-66.
• Imre Kátai, On a problem of A. Ivic, Mathematica Pannonica, Vol. 18, No. 1 (2007), pp. 11-18.

Crossrefs

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

Programs

Mathematica

Table[DivisorSigma[0, n + DivisorSigma[0, n]], {n, 117}] (* Michael De Vlieger, May 21 2017 *)

PARI

A286529(n) = numdiv(n+numdiv(n));

Python

from sympy import divisor_count as d
def a(n): return d(n + d(n)) # Indranil Ghosh, May 21 2017

Scheme

(define (A286529 n) (A000005 (+ n (A000005 n))))

Formula

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

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