OFFSET
1,2
COMMENTS
For example, 182 is the Heinz number of (6,4,1) with product 24 and conjugate (3,2,2,2,1,1) with product also 24.
The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1) * ... * prime(y_k).
The enumeration of these partitions by sum is given by A325039.
EXAMPLE
The sequence of terms together with their prime indices begins:
1: {}
2: {1}
6: {1,2}
9: {2,2}
20: {1,1,3}
30: {1,2,3}
49: {4,4}
56: {1,1,1,4}
70: {1,3,4}
75: {2,3,3}
81: {2,2,2,2}
84: {1,1,2,4}
90: {1,2,2,3}
125: {3,3,3}
176: {1,1,1,1,5}
182: {1,4,6}
210: {1,2,3,4}
264: {1,1,1,2,5}
350: {1,3,3,4}
416: {1,1,1,1,1,6}
MATHEMATICA
priptn[n_]:=If[n==1, {}, Reverse[Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]];
conj[y_]:=If[Length[y]==0, y, Table[Length[Select[y, #>=k&]], {k, 1, Max[y]}]];
Select[Range[100], Times@@priptn[#]==Times@@conj[priptn[#]]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 25 2019
STATUS
approved