A317749 - OEIS

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

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OFFSET

1,2

COMMENTS

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

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

LINKS

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

FORMULA

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

EXAMPLE

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.

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 *)

PROG

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

CROSSREFS

Cf. A000005, A128863, A049820, A189827.

Sequence in context: A296372 A278300 A034214 * A253415 A227401 A131813

Adjacent sequences: A317746 A317747 A317748 * A317750 A317751 A317752

KEYWORD

nonn

AUTHOR

Jinyuan Wang, Aug 06 2018

EXTENSIONS

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

STATUS

approved