A329656 Starting at k = A001414(n), iterate k -> n mod k until k=0. a(n) is the number of steps taken.

0, 1, 1, 1, 1, 2, 1, 2, 2, 3, 1, 3, 1, 4, 3, 1, 1, 2, 1, 2, 2, 4, 1, 2, 2, 4, 1, 3, 1, 1, 1, 2, 3, 4, 4, 2, 1, 4, 4, 3, 1, 2, 1, 3, 2, 4, 1, 2, 2, 2, 5, 2, 1, 4, 4, 2, 5, 4, 1, 1, 1, 4, 4, 2, 4, 2, 1, 4, 3, 1, 1, 1, 1, 4, 3, 4, 4, 2, 1, 2, 2, 4, 1, 1, 5, 4, 6, 3, 1, 3, 4, 3, 4, 4, 5, 3, 1, 2, 3

Offset

1,6

Comments

If n is prime, a(n)=1.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

A001414(6) = 2+3 = 5, 6 mod 5 = 1, 6 mod 1 = 0 so a(6) = 2.

Maple

f:= proc(n) local s, t;
s:= convert(map(convert, ifactors(n)[2], `*`), `+`);
for t from 1 do
  s:= n mod s;
  if s = 0 then return t fi
od
end proc:
f(1):= 0:
map(f, [$1..200]);

Mathematica

sopfr[n_] := If[n == 1, 0, Total[Times @@@ FactorInteger[n]]];
f[n_] := Module[{s, t}, s = sopfr[n]; For[t = 1, True, t++, s = Mod[n, s]; If[s == 0, Return [t]]]]; f[1] = 0;
Array[f, 200] (* Jean-François Alcover, Aug 22 2020, after Maple *)

Crossrefs

Cf. A001414.

Sequence in context: A176853 A261787 A302480 * A000374 A355735 A355733

Adjacent sequences: A329653 A329654 A329655 * A329657 A329658 A329659

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Nov 18 2019

Status

approved