A066925 - OEIS

%I #14 Jul 16 2021 13:15:34

%S 1,4,9,16,18,24,25,30,36,40,48,49,64,70,72,81,84,90,96,100,108,112,

%T 120,121,126,144,150,154,160,162,168,169,180,192,196,198,204,208,210,

%U 216,220,225,228,234,240,250,252,256,264,270,276,280,286,288,289,294

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

%H Giovanni Resta, <a href="/A066925/b066925.txt">Table of n, a(n) for n = 1..1000</a>

%e 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.

%t 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]

%Y Cf. A066926.

%K nonn,nice

%O 1,2

%A _David Eppstein_, Jan 23 2002

%E More terms from _Dean Hickerson_, Jan 27 2002