OFFSET
0,5
LINKS
Chai Wah Wu, Table of n, a(n) for n = 0..59
EXAMPLE
The a(8) = 17 integer partitions:
(53), (62), (71),
(332), (422), (431), (521), (611),
(3221), (4211), (5111),
(22211), (32111), (41111),
(221111), (311111),
(2111111).
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/@#&];
Table[Length[Select[IntegerPartitions[n], Select[ptnmats[Times@@Prime/@#], And[SameQ@@Total/@#, SameQ@@Total/@Transpose[#]]&]=={}&]], {n, 10}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 13 2019
EXTENSIONS
a(17)-a(53) from Chai Wah Wu, Jan 15 2019
STATUS
approved