OFFSET
1,1
COMMENTS
The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
The Durfee square of an integer partition is the largest square contained in its Young diagram.
LINKS
EXAMPLE
The sequence of terms together with their prime indices begins:
125: {3,3,3}
175: {3,3,4}
245: {3,4,4}
250: {1,3,3,3}
275: {3,3,5}
325: {3,3,6}
343: {4,4,4}
350: {1,3,3,4}
375: {2,3,3,3}
385: {3,4,5}
425: {3,3,7}
455: {3,4,6}
475: {3,3,8}
490: {1,3,4,4}
500: {1,1,3,3,3}
525: {2,3,3,4}
539: {4,4,5}
550: {1,3,3,5}
575: {3,3,9}
595: {3,4,7}
MATHEMATICA
durf[n_]:=Length[Select[Range[PrimeOmega[n]], Reverse[Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]][[#]]>=#&]];
Select[Range[100], durf[#]==3&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 06 2019
STATUS
approved