OFFSET
1,1
COMMENTS
The enumeration of these partitions by sum is given by A325181.
The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
LINKS
EXAMPLE
The sequence of terms together with their prime indices begins:
3: {2}
4: {1,1}
6: {1,2}
15: {2,3}
18: {1,2,2}
25: {3,3}
27: {2,2,2}
30: {1,2,3}
45: {2,2,3}
50: {1,3,3}
75: {2,3,3}
175: {3,3,4}
245: {3,4,4}
250: {1,3,3,3}
343: {4,4,4}
350: {1,3,3,4}
375: {2,3,3,3}
490: {1,3,4,4}
525: {2,3,3,4}
625: {3,3,3,3}
MATHEMATICA
durf[n_]:=Length[Select[Range[PrimeOmega[n]], Reverse[Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]][[#]]>=#&]];
codurf[n_]:=If[n==1, 0, Max[PrimeOmega[n], PrimePi[FactorInteger[n][[-1, 1]]]]];
Select[Range[1000], codurf[#]-durf[#]==1&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 08 2019
STATUS
approved