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A323304 Heinz numbers of integer partitions that cannot be arranged into a matrix with equal row-sums and equal column-sums. 4
6, 10, 12, 14, 15, 18, 20, 21, 22, 24, 26, 28, 30, 33, 34, 35, 38, 39, 40, 42, 44, 45, 46, 48, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 102, 104, 105 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The first term of this sequence absent from A106543 is 144.

The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).

LINKS

Table of n, a(n) for n=1..65.

Index entries for sequences related to Heinz numbers

MATHEMATICA

primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];

facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]];

ptnmats[n_]:=Union@@Permutations/@Select[Union@@(Tuples[Permutations/@#]&/@Map[primeMS, facs[n], {2}]), SameQ@@Length/@#&];

Select[Range[2, 1000], Select[ptnmats[#], And[SameQ@@Total/@#, SameQ@@Total/@Transpose[#]]&]=={}&]

CROSSREFS

Complement of A323306.

Cf. A006052, A007016, A008480, A056239, A112798, A120733, A319056, A321719, A321721.

Cf. A323300, A323302, A323305, A323347, A323348,  A323349.

Sequence in context: A168638 A024619 A335080 * A325411 A106543 A324455

Adjacent sequences:  A323301 A323302 A323303 * A323305 A323306 A323307

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jan 13 2019

STATUS

approved

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Last modified April 17 03:58 EDT 2021. Contains 343059 sequences. (Running on oeis4.)