A071375 Smallest m such that sum of squarefree divisors of m equals n; a(n) = 0 if no solution to A048250(x) = n exists.

1, 0, 2, 3, 0, 5, 0, 7, 0, 0, 0, 6, 0, 13, 0, 0, 0, 10, 0, 19, 0, 0, 0, 14, 0, 0, 0, 0, 0, 29, 0, 21, 0, 0, 0, 22, 0, 37, 0, 0, 0, 26, 0, 43, 0, 0, 0, 33, 0, 0, 0, 0, 0, 34, 0, 39, 0, 0, 0, 38, 0, 61, 0, 0, 0, 0, 0, 67, 0, 0, 0, 30, 0, 73, 0, 0, 0, 0, 0, 57, 0, 0, 0, 65, 0, 0, 0, 0, 0, 58, 0, 0, 0, 0

Offset: 1

Author

Labos Elemer, May 22 2002

Keywords

• nonn

Examples

			n=256: a(256)=217=7.31, all divisors are squarefree and 1+7+31+217=256=n.
		

Crossrefs

Cf. A048250.

Programs

Mathematica

ffi[x_] := Flatten[FactorInteger[x]] lf[x_] := Length[FactorInteger[x]] ba[x_] := Table[Part[ffi[x], 2 * w - 1], {w, 1, lf[x]}] cor[x_] := Apply[Times, ba[x]] t = Table[0, {256}]; Do[s = DivisorSigma[1, cor[n]]; If[s < 257 && t[[s]] == 0, t[[s]] = n], {n, 10^6}]; t

Formula

a(n)=Min{x; A048250[x]=n}, a(n)=0 if no solutions.

Extensions

Definition corrected by Jaroslav Krizek, May 28 2014