OFFSET
1,1
COMMENTS
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 A006918 (see Emeric Deutsch's comment there).
EXAMPLE
The sequence of terms together with their prime indices begins:
27: {2,2,2}
45: {2,2,3}
54: {1,2,2,2}
63: {2,2,4}
75: {2,3,3}
81: {2,2,2,2}
90: {1,2,2,3}
99: {2,2,5}
105: {2,3,4}
108: {1,1,2,2,2}
117: {2,2,6}
126: {1,2,2,4}
135: {2,2,2,3}
147: {2,4,4}
150: {1,2,3,3}
153: {2,2,7}
162: {1,2,2,2,2}
165: {2,3,5}
171: {2,2,8}
180: {1,1,2,2,3}
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], PrimeOmega[#]>=3&&Reverse[primeMS[#]][[3]]==2&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 05 2019
STATUS
approved