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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 (list; graph; refs; listen; history; text; internal format)
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: A321297 A163577 A132178 * A103775 A331594 A093057

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

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Last modified April 8 23:02 EDT 2020. Contains 333331 sequences. (Running on oeis4.)