A140523 If the highest power of the prime p that divides n is p^b(n,p), then a(n) is the least nonnegative integer that equals some sum{p|n} (+or-)p^b(n, p).

0, 2, 3, 4, 5, 1, 7, 8, 9, 3, 11, 1, 13, 5, 2, 16, 17, 7, 19, 1, 4, 9, 23, 5, 25, 11, 27, 3, 29, 0, 31, 32, 8, 15, 2, 5, 37, 17, 10, 3, 41, 2, 43, 7, 4, 21, 47, 13, 49, 23, 14, 9, 53, 25, 6, 1, 16, 27, 59, 2, 61, 29, 2, 64, 8, 6, 67, 13, 20, 0, 71, 1, 73, 35, 22, 15, 4, 8, 79, 11, 81, 39, 83

Offset

1,2

Links

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

Example

60 has the prime factorization: 2^2 * 3^1 * 5^1. The least nonnegative integer that is made by either adding or subtracting the prime powers in this prime factorization is: a(60) = + 2^2 + 3^1 - 5^1 = 2.

Maple

f:= proc(n) local F, V, i;
  F:= map(t -> t[1]^t[2], ifactors(n)[2]);
  V:= {F[1]};
  for i from 2 to nops(F) do
    V:= map(t -> (t+F[i], t-F[i]), V);
  od:
  min(map(abs, V))
end proc:
f(1):= 0:
map(f, [$1..100]); # Robert Israel, Sep 12 2018

Mathematica

f[n_] := Module[{F, V}, F = Power @@@ FactorInteger[n]; V = {F[[1]]}; Do[V = {# + F[[i]], # - F[[i]]}& /@ V // Flatten, {i, 2, Length[F]}]; V // Abs // Min];
f[1] = 0;
Array[f, 100] (* Jean-François Alcover, Aug 28 2020, after Robert Israel *)

Crossrefs

Sequence in context: A241479 A100994 A375228 * A237517 A332883 A017666

Adjacent sequences: A140520 A140521 A140522 * A140524 A140525 A140526

Keyword

nonn

Author

Leroy Quet, Jul 02 2008

Extensions

Extended by Ray Chandler, Jun 25 2009

Status

approved