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 A326852.
EXAMPLE
The sequence of terms together with their prime indices begins:
30: {1,2,3}
84: {1,1,2,4}
264: {1,1,1,2,5}
273: {2,4,6}
286: {1,5,6}
325: {3,3,6}
351: {2,2,2,6}
364: {1,1,4,6}
390: {1,2,3,6}
441: {2,2,4,4}
490: {1,3,4,4}
525: {2,3,3,4}
624: {1,1,1,1,2,6}
756: {1,1,2,2,2,4}
784: {1,1,1,1,4,4}
810: {1,2,2,2,2,3}
840: {1,1,1,2,3,4}
874: {1,8,9}
900: {1,1,2,2,3,3}
988: {1,1,6,8}
MATHEMATICA
Select[Range[1000], With[{y=Flatten[Cases[FactorInteger[#], {p_, k_}:>Table[PrimePi[p], {k}]]]}, !SameQ@@y&&Divisible[Total[y], Max[y]]&&Divisible[Total[y], Length[y]]]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 26 2019
STATUS
approved