A317749 a(n+1) = d(n) + d(a(n)) with a(1)=1, where d(n) is the number of the divisors of n.

1, 2, 4, 5, 5, 4, 7, 4, 7, 5, 6, 6, 10, 6, 8, 8, 9, 5, 8, 6, 10, 8, 8, 6, 12, 9, 7, 6, 10, 6, 12, 8, 10, 8, 8, 8, 13, 4, 7, 6, 12, 8, 12, 8, 10, 10, 8, 6, 14, 7, 8, 8, 10, 6, 12, 10, 12, 10, 8, 6, 16, 7, 6, 10, 11, 6, 12, 8, 10, 8, 12, 8, 16, 7, 6, 10, 10, 8, 12, 8, 14, 9, 7, 4, 15, 8, 8, 8, 12, 8, 16, 9, 9, 7, 6, 8, 16, 7, 8, 10

Offset: 1

Author

Jinyuan Wang, Aug 06 2018

Keywords

• nonn

Comments

If a(n+1)=4, then n and a(n) are prime numbers.

a(n+1) < 2*sqrt(a(n)) + 2*sqrt(n).

Examples

			d(1) = 1, d(2) = 2, d(3) = 2; a(1) = 1, a(2) = 2, a(3) = 4.
a(38)=4, so 37 and a(37)=13 are prime numbers.
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A128863, A049820, A189827.

Programs

Mathematica

a[n_] := DivisorSigma[0, n - 1] + DivisorSigma[0, a[n - 1]]; a[1] = 1; Array[a, 80] (* Robert G. Wilson v, Aug 06 2018 *)

PARI

a(n) = if (n==1, 1, numdiv(n-1) + numdiv(a(n-1))); \\ Michel Marcus, Aug 25 2018

Formula

a(n+1) = d(n) + d(a(n)) where d(n) is the number of divisors of n (A000005).

Extensions

Name edited by and more terms from Robert G. Wilson v, Aug 06 2018