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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 (list; graph; refs; listen; history; text; internal format)
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. Adams-Watters, May 10 2010]

LINKS

Franklin T. Adams-Watters, 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. Adams-Watters, May 10 2010

CROSSREFS

Cf. A039649-A039656.

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. Adams-Watters, May 10 2010

STATUS

approved

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Last modified March 30 18:30 EDT 2017. Contains 284302 sequences.