

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



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(n1) + numdiv(a(n1))); \\ 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



