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 A320922 Heinz numbers of graphical partitions. 37
 1, 4, 12, 16, 27, 36, 40, 48, 64, 81, 90, 108, 112, 120, 144, 160, 192, 225, 243, 252, 256, 270, 300, 324, 336, 352, 360, 400, 432, 448, 480, 567, 576, 625, 630, 640, 675, 729, 750, 756, 768, 792, 810, 832, 840, 900, 972, 1000, 1008, 1024, 1056, 1080, 1120 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k). An integer partition is graphical if it comprises the vertex-degrees of some simple graph. LINKS Table of n, a(n) for n=1..53. EXAMPLE The sequence of all graphical partitions begins: (), (11), (211), (1111), (222), (2211), (3111), (21111), (111111), (2222), (3221), (22211), (41111), (32111), (221111), (311111), (2111111), (3322), (22222), (42211). MATHEMATICA prptns[m_]:=Union[Sort/@If[Length[m]==0, {{}}, Join@@Table[Prepend[#, m[[ipr]]]&/@prptns[Delete[m, List/@ipr]], {ipr, Select[Prepend[{#}, 1]&/@Select[Range[2, Length[m]], m[[#]]>m[[#-1]]&], UnsameQ@@m[[#]]&]}]]]; Select[Range[1000], Select[prptns[Flatten[MapIndexed[Table[#2, {#1}]&, If[#==1, {}, Flatten[Cases[FactorInteger[#], {p_, k_}:>Table[PrimePi[p], {k}]]]]]]], UnsameQ@@#&]!={}&] CROSSREFS Cf. A000070, A000569, A007717, A056239, A096373, A112798, A147878, A209816, A300061, A320458, A320911, A320923, A320924. Sequence in context: A187084 A090818 A075191 * A028594 A239050 A152680 Adjacent sequences: A320919 A320920 A320921 * A320923 A320924 A320925 KEYWORD nonn AUTHOR Gus Wiseman, Oct 24 2018 STATUS approved

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Last modified April 19 12:14 EDT 2024. Contains 371792 sequences. (Running on oeis4.)