OFFSET
1,1
COMMENTS
A finite multiset of numbers is defined to be triquanimous iff it can be partitioned into three multisets with equal sums.
A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
EXAMPLE
The terms together with their prime indices begin:
8: {1,1,1}
27: {2,2,2}
36: {1,1,2,2}
48: {1,1,1,1,2}
64: {1,1,1,1,1,1}
125: {3,3,3}
150: {1,2,3,3}
180: {1,1,2,2,3}
200: {1,1,1,3,3}
216: {1,1,1,2,2,2}
240: {1,1,1,1,2,3}
288: {1,1,1,1,1,2,2}
320: {1,1,1,1,1,1,3}
343: {4,4,4}
384: {1,1,1,1,1,1,1,2}
441: {2,2,4,4}
490: {1,3,4,4}
512: {1,1,1,1,1,1,1,1,1}
567: {2,2,2,2,4}
588: {1,1,2,4,4}
MATHEMATICA
hwt[n_]:=Total[Cases[FactorInteger[n], {p_, k_}:>PrimePi[p]*k]];
facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]];
Select[Range[1000], Select[facs[#], Length[#]==3&&SameQ@@hwt/@#&]!={}&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 19 2024
STATUS
approved