A238529 a(0) = a(1) = 0, and for n > 1, a(n) = number of iterations of A238525 (n modulo sopfr(n)) needed to reach either 0 or 1. Here sopfr(n) is the sum of the prime factors of n, with multiplicity, A001414.

0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 1, 3, 1, 2, 2, 2, 1, 2, 1, 1, 1, 2, 2, 3, 2, 2, 1, 2, 2, 2, 1, 2, 1, 3, 1, 2, 1, 2, 2, 2, 2, 1, 1, 3, 2, 2, 2, 2, 1, 1, 1, 2, 2, 2, 2, 2, 1, 2, 2, 1, 1, 1, 1, 3, 3, 2, 2, 2, 1, 2, 3, 3, 1, 1, 2, 2, 2, 2, 1, 3, 2, 2, 3, 2, 2, 2, 1, 2, 3, 2, 1, 3, 1, 3, 1

Offset

0,9

Comments

Previous name was: Recursive depth of n modulo sopfr(n), where sopfr(n) is the sum of the prime factors of n, with multiplicity.

Indices of records are 0, 2, 8, 22, 166, ... (A238530) - David A. Corneth & Antti Karttunen, Oct 20 2017

Links

Antti Karttunen, Table of n, a(n) for n = 0..16384

Formula

a(0) = a(1) = 0; for n > 1, a(n) = 1 + a(A238525(n)). - Antti Karttunen, Oct 20 2017

Example

a(2) = 1, because 2 mod sopfr(2) = 2 mod 2 = 0, and further recursion (0 mod sopfr(0)) is undefined.
a(8) = 2, because 8 mod sopfr(8) = 8 mod 6 = 2, and 2 mod sopfr(2) is defined as above, giving 8 a recursive depth of 2.

Mathematica

Array[-1 + Length@ NestWhileList[Mod[#, Total@ Flatten@ Map[ConstantArray[#1, #2] & @@ # &, FactorInteger@ #]] &, #, # > 1 &] &, 105, 0] (* Michael De Vlieger, Oct 20 2017 *)

Prog

(Sage)
def a(n):
    d = 0
    while n>1:
        n = n % sum([f[0]*f[1] for f in factor(n)])
        d = d+1
   return d
# Ralf Stephan, Mar 09 2014
(PARI)
A001414(n) = { my(f=factor(n)); sum(k=1, matsize(f)[1], f[k, 1]*f[k, 2]); };
A238525(n) = (n%A001414(n));
A238529(n) = if(n<=1, 0, 1+A238529(A238525(n))); \\ Antti Karttunen, Oct 20 2017

Crossrefs

Cf. A001414, A238525, A238530.

Sequence in context: A105971 A280314 A080354 * A195150 A022307 A029413

Adjacent sequences: A238526 A238527 A238528 * A238530 A238531 A238532

Keyword

nonn

Author

J. Stauduhar, Feb 28 2014

Extensions

More terms from Ralf Stephan, Mar 09 2014

Terms a(0) = a(1) = 0 prepended and name changed by Antti Karttunen, Oct 20 2017

Status

approved