A066925 Numbers k having a partition k = sum x_i for which sum k/x_i is the same partition of k.

1, 4, 9, 16, 18, 24, 25, 30, 36, 40, 48, 49, 64, 70, 72, 81, 84, 90, 96, 100, 108, 112, 120, 121, 126, 144, 150, 154, 160, 162, 168, 169, 180, 192, 196, 198, 204, 208, 210, 216, 220, 225, 228, 234, 240, 250, 252, 256, 264, 270, 276, 280, 286, 288, 289, 294

Offset

1,2

Links

Giovanni Resta, Table of n, a(n) for n = 1..1000

Example

24 is in the sequence because 24 = 2+4+6+12 and 12/2 + 12/4 + 12/6 + 12/12 gives the same partition 2+4+6+12.

Mathematica

SelfInvPart[n_, x_, terms_] := If[Length[terms]==0||x<0, False, If[x==0, True, If[IntegerQ[Sqrt[n]]&&SelfInvPart[n, x-Sqrt[n], terms], True, If[IntegerQ[n/First[terms]]&&SelfInvPart[n, x-First[terms]-n/First[terms], terms], True, SelfInvPart[n, x, Rest[terms]]]]]]; TestSelfInv[n_] := SelfInvPart[n, n, Divisors[n]]; Select[Range[100], TestSelfInv]

Crossrefs

Cf. A066926.

Sequence in context: A313319 A313320 A066926 * A313321 A313322 A122379

Adjacent sequences: A066922 A066923 A066924 * A066926 A066927 A066928

Keyword

nonn,nice

Author

David Eppstein, Jan 23 2002

Extensions

More terms from Dean Hickerson, Jan 27 2002

Status

approved