

A039655


Number of iterations of f(x) = sigma(x)1 applied to n required to reach a prime, or 1 if no prime is ever reached.


14



0, 0, 2, 0, 1, 0, 2, 5, 1, 0, 4, 0, 1, 1, 2, 0, 2, 0, 1, 1, 2, 0, 1, 2, 1, 3, 2, 0, 1, 0, 5, 1, 1, 1, 2, 0, 1, 2, 1, 0, 4, 0, 1, 5, 1, 0, 2, 4, 2, 1, 1, 0, 3, 1, 3, 1, 1, 0, 1, 0, 4, 1, 2, 1, 2, 0, 3, 4, 2, 0, 2, 0, 1, 2, 1, 4, 1, 0, 2, 2, 3, 0, 1, 1, 1, 3, 1, 0, 1, 2, 1, 1, 2, 3, 1, 0, 3, 2, 2, 0, 2, 0, 2, 1, 2
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OFFSET

2,3


LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 2..10000
MathOverflow, Does iterating a certain function related to the sums of divisors eventually always result in a prime value?, 2014
Hugo Pfoertner, Terms a(2)...a(1000000).
N. J. A. Sloane, Three (No, 8) Lovely Problems from the OEIS, Experimental Mathematics Seminar, Rutgers University, Oct 05 2017, Part I, Part 2, Slides. (Mentions this sequence)


MATHEMATICA

f[n_] := Plus @@ Divisors@n  1; g[n_] := Length@ NestWhileList[ f@# &, n, !PrimeQ@# &]  1; Table[ g@n, {n, 2, 106}] (* Robert G. Wilson v, May 07 2010 *)


PROG

(PARI) a(n)=my(t); while(!isprime(n), n=sigma(n)1; t++); t \\ Charles R Greathouse IV, Sep 16 2014


CROSSREFS

Cf. A039654, A039649, A039650, A039651, A039652, A039653, A039655, A039656.
For records see A292114 and A292115.
Sequence in context: A163577 A132178 A357869 * A357882 A103775 A331594
Adjacent sequences: A039652 A039653 A039654 * A039656 A039657 A039658


KEYWORD

nonn


AUTHOR

David W. Wilson


EXTENSIONS

Escape clause added by N. J. A. Sloane, Aug 31 2017


STATUS

approved



