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.
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
Offset: 2
Keywords
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)
Crossrefs
Programs
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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 *) -
PARI
a(n)=my(t);while(!isprime(n),n=sigma(n)-1;t++);t \\ Charles R Greathouse IV, Sep 16 2014
Extensions
Escape clause added by N. J. A. Sloane, Aug 31 2017
Comments