A323304 Heinz numbers of integer partitions that cannot be arranged into a matrix with equal row-sums and equal column-sums.

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

Offset: 1

Author

Gus Wiseman, Jan 13 2019

Keywords

• nonn

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

• Index entries for sequences related to Heinz numbers

Crossrefs

Complement of A323306.

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

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

Programs

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[#]]&]=={}&]