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A140523
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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).
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1
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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
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OFFSET
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1,2
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LINKS
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EXAMPLE
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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.
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MAPLE
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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:
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MATHEMATICA
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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;
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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