

A039654


Prime reached by iterating f(x) = sigma(x)1 on n, or zero if no prime is ever reached.


2



2, 3, 11, 5, 11, 7, 23, 71, 17, 11, 71, 13, 23, 23, 71, 17, 59, 19, 41, 31, 47, 23, 59, 71, 41, 71, 71, 29, 71, 31, 167, 47, 53, 47, 233, 37, 59, 71, 89, 41, 167, 43, 83, 167, 71, 47, 167, 167, 167, 71, 97, 53, 167, 71, 167, 79, 89, 59, 167, 61, 167, 103, 311, 83, 167, 67
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OFFSET

2,1


COMMENTS

It appears nearly certain that a prime is always reached for n>1.
Since sigma(n) > n for n > 1, and sigma(n) = n + 1 only for n prime, the iteration either reaches a prime and loops there, or grows indefinitely. [Franklin T. AdamsWatters, May 10 2010]


LINKS

Franklin T. AdamsWatters, Table of n, a(n) for n=2..10000
Math Overflow discussion, Does iterating a certain function related to the sums of divisors eventually always result in a prime value?


MATHEMATICA

f[n_]:=Plus@@Divisors[n]1; Table[Nest[f, n, 6], {n, 2, 5!}] (* Vladimir Joseph Stephan Orlovsky, Mar 10 2010 *)
f[n_] := DivisorSigma[1, n]1; Table[FixedPoint[f, n], {n, 2, 100}] (* T. D. Noe, May 10 2010 *)


PROG

(PARI) a(n)=local(m); if(n<2, 0, while((m=sigma(n)1)!=n, n=m); n) \\ Franklin T. AdamsWatters, May 10 2010


CROSSREFS

Cf. A039649A039656.
Sequence in context: A084743 A030391 A244496 * A075240 A229607 A137332
Adjacent sequences: A039651 A039652 A039653 * A039655 A039656 A039657


KEYWORD

nonn


AUTHOR

David W. Wilson


EXTENSIONS

Contingency for no prime reached added by Franklin T. AdamsWatters, May 10 2010


STATUS

approved



