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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

%I

%S 1,4,9,16,18,24,25,30,36,40,48,49,60,64,70,72,81,84,90,96,100,105,108,

%T 112,120,121,126,132,144,150,154,156,160,162,168,169,180,192,196,198,

%U 204,208,210,216,220,225,228,234,240,250,252,256,264,270,273,276,280

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

%C Each k/x_i must be an integer. - _Harvey P. Dale_, Dec 27 2018

%H Giovanni Resta, <a href="/A066926/b066926.txt">Table of n, a(n) for n = 1..350</a>

%e 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.

%t 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]

%o (Haskell)

%o a066926 n = a066926_list !! (n-1)

%o a066926_list = filter f [1..] where

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

%o ps u 0 = [[]]

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

%o -- _Reinhard Zumkeller_, Jun 07 2015

%Y Cf. A066925.

%K nonn,nice

%O 1,2

%A _David Eppstein_, Jan 23 2002

%E More terms from _Dean Hickerson_, Jan 27 2002

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Last modified September 16 16:40 EDT 2021. Contains 347473 sequences. (Running on oeis4.)