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0, 4, 9, 16, 25, 13, 49, 64, 81, 29, 121, 25, 169, 53, 34, 256, 289, 85, 361, 41, 58, 125, 529, 73, 625, 173, 729, 65, 841, 38, 961, 1024, 130, 293, 74, 97, 1369, 365, 178, 89, 1681, 62, 1849, 137, 106, 533, 2209, 265, 2401, 629, 298, 185, 2809, 733, 146, 113
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OFFSET
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1,2
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LINKS
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FORMULA
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Additive with a(p^e) = p^(2e).
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EXAMPLE
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a(1) = 0 since 1 has no prime factor; n = p^2: a(p^2) = p^2; n = 6: a(6) = 4+9 = 13; a(u*w) = a(u)+a(w) if gcd(u,w) = 1; a(21) = a(7)+a(3) = 49+9 = 58; additive with respect of unitary prime divisor decompositions.
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MAPLE
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a:= n-> add(i[1]^i[2], i=ifactors(n^2)[2]):
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MATHEMATICA
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ffi[x_] := Flatten[FactorInteger[x]] lf[x_] := Length[FactorInteger[x]] ba[x_] := Table[Part[ffi[x], 2*w-1], {w, 1, lf[x]}] ep[x_] := Table[Part[ffi[x], 2*w], {w, 1, lf[x]}] supo[x_] := Apply[Plus, ba[x]^ep[x]] Table[supo[w], {w, 1, 25}]
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PROG
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(PARI) f(n) = { my(f=factor(n)); vecsum(vector(#f~, i, f[i, 1]^f[i, 2])); }; \\ A008475
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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