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

Author

David W. Wilson

Keywords

• nonn

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

Cf. A039654, A039649, A039650, A039651, A039652, A039653, A039655, A039656.

For records see A292114 and A292115.

Programs

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