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
Examples
a(6) = 1, because 6 mod sopfr(6) = 6 mod 5 = 1.
Links
- Reinhard Zumkeller, Table of n, a(n) for n = 2..10000
Programs
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Haskell
a238525 n = mod n $ a001414 n -- Reinhard Zumkeller, Jul 21 2014
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Mathematica
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 *)
Formula
a(n) = n mod A001414(n).
Comments