A238530 -id:A238530 - cp's OEIS frontend

A238525 n modulo sopfr(n), where sopfr(n) is the sum of the prime factors of n, with multiplicity.

0, 0, 0, 0, 1, 0, 2, 3, 3, 0, 5, 0, 5, 7, 0, 0, 2, 0, 2, 1, 9, 0, 6, 5, 11, 0, 6, 0, 0, 0, 2, 5, 15, 11, 6, 0, 17, 7, 7, 0, 6, 0, 14, 1, 21, 0, 4, 7, 2, 11, 1, 0, 10, 7, 4, 13, 27, 0, 0, 0, 29, 11, 4, 11, 2, 0, 5, 17, 0, 0, 0, 0, 35, 10, 7, 5, 6, 0, 2, 9, 39

Offset: 2

J. Stauduhar, Feb 28 2014

a(A036844(n)) = 0. - Reinhard Zumkeller, Jul 21 2014

			a(6) = 1, because 6 mod sopfr(6) = 6 mod 5 = 1.

Reinhard Zumkeller, Table of n, a(n) for n = 2..10000

Cf. A001414, A238526, A238527, A238528, A238529, A238530.

Cf. A036844.

a238525 n = mod n $ a001414 n  -- Reinhard Zumkeller, Jul 21 2014

Table[Mod[n, Apply[Dot, Transpose[FactorInteger[n]]]], {n, 105}] (* Wouter Meeussen, Mar 01 2014 *)
mms[n_]:=Mod[n,Total[Flatten[Table[#[[1]],#[[2]]]&/@FactorInteger[ n]]]]; Array[mms,90,2] (* Harvey P. Dale, May 25 2016 *)

a(n) = n mod A001414(n).

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.

Original entry on oeis.org

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

J. Stauduhar, Feb 28 2014

nonn

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

			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.

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

Cf. A001414, A238525, A238530.

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

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

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

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

More terms from Ralf Stephan, Mar 09 2014

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

cp's OEIS Frontend

A238525 n modulo sopfr(n), where sopfr(n) is the sum of the prime factors of n, with multiplicity.

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