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A066926 Numbers k having a partition k = sum x_i for which sum k/x_i is also a partition of k. 5
1, 4, 9, 16, 18, 24, 25, 30, 36, 40, 48, 49, 60, 64, 70, 72, 81, 84, 90, 96, 100, 105, 108, 112, 120, 121, 126, 132, 144, 150, 154, 156, 160, 162, 168, 169, 180, 192, 196, 198, 204, 208, 210, 216, 220, 225, 228, 234, 240, 250, 252, 256, 264, 270, 273, 276, 280 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Each k/x_i must be an integer. - Harvey P. Dale, Dec 27 2018

LINKS

Giovanni Resta, Table of n, a(n) for n = 1..350

EXAMPLE

60 is in the sequence because 60 has a partition 4+5+5+10+12+12+12 for which 60/4 + 60/5 + 60/5 + 60/10 + 60/12 + 60/12 + 60/12 = 5+5+5+6+12+12+15 is also a partition of 60.

MATHEMATICA

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

PROG

(Haskell)

a066926 n = a066926_list !! (n-1)

a066926_list = filter f [1..] where

   f x = elem x $ map sum $ map (map (div x)) $ ps 1 x where

     ps u 0 = [[]]

     ps u v = [t:ts | t <- [u..v], t > 1, mod x t == 0, ts <- ps t (v - t)]

-- Reinhard Zumkeller, Jun 07 2015

CROSSREFS

Cf. A066925.

Sequence in context: A336919 A313319 A313320 * A066925 A313321 A313322

Adjacent sequences:  A066923 A066924 A066925 * A066927 A066928 A066929

KEYWORD

nonn,nice

AUTHOR

David Eppstein, Jan 23 2002

EXTENSIONS

More terms from Dean Hickerson, Jan 27 2002

STATUS

approved

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Last modified August 2 05:02 EDT 2021. Contains 346409 sequences. (Running on oeis4.)