OFFSET
1,2
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 A325325.
LINKS
EXAMPLE
Most small numbers are in the sequence, but the sequence of non-terms together with their prime indices begins:
8: {1,1,1}
16: {1,1,1,1}
24: {1,1,1,2}
27: {2,2,2}
30: {1,2,3}
32: {1,1,1,1,1}
36: {1,1,2,2}
40: {1,1,1,3}
48: {1,1,1,1,2}
54: {1,2,2,2}
56: {1,1,1,4}
60: {1,1,2,3}
64: {1,1,1,1,1,1}
72: {1,1,1,2,2}
80: {1,1,1,1,3}
81: {2,2,2,2}
88: {1,1,1,5}
90: {1,2,2,3}
96: {1,1,1,1,1,2}
100: {1,1,3,3}
MATHEMATICA
primeptn[n_]:=If[n==1, {}, Reverse[Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]];
Select[Range[100], UnsameQ@@Differences[primeptn[#]]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 02 2019
STATUS
approved