OFFSET
1,2
COMMENTS
The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), so these are numbers of the form Product_{k = 1...b} prime(k * c) for some b > 1 and c > 0.
EXAMPLE
The sequence of terms together with their prime indices begins:
1: {}
6: {1,2}
21: {2,4}
30: {1,2,3}
65: {3,6}
133: {4,8}
210: {1,2,3,4}
273: {2,4,6}
319: {5,10}
481: {6,12}
731: {7,14}
1007: {8,16}
1403: {9,18}
1495: {3,6,9}
2059: {10,20}
2310: {1,2,3,4,5}
2449: {11,22}
3293: {12,24}
4141: {13,26}
4601: {14,28}
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[10000], !PrimeQ[#]&&SameQ@@Differences[Prepend[primeMS[#], 0]]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 03 2019
STATUS
approved