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 A325164 Heinz numbers of integer partitions with Durfee square of length 2. 13
 9, 15, 18, 21, 25, 27, 30, 33, 35, 36, 39, 42, 45, 49, 50, 51, 54, 55, 57, 60, 63, 65, 66, 69, 70, 72, 75, 77, 78, 81, 84, 85, 87, 90, 91, 93, 95, 98, 99, 100, 102, 105, 108, 110, 111, 114, 115, 117, 119, 120, 121, 123, 126, 129, 130, 132, 133, 135, 138, 140 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). Also positions of 2 in A257990. First differs from A105441 in lacking 125. The Durfee length 1 case is A093641. The enumeration of Durfee length 2 partitions by sum is given by A006918, while that of Durfee length 3 partitions is given by A117485. LINKS Gus Wiseman, Young diagrams corresponding to the first 36 terms. EXAMPLE The sequence of terms together with their prime indices begins:    9: {2,2}   15: {2,3}   18: {1,2,2}   21: {2,4}   25: {3,3}   27: {2,2,2}   30: {1,2,3}   33: {2,5}   35: {3,4}   36: {1,1,2,2}   39: {2,6}   42: {1,2,4}   45: {2,2,3}   49: {4,4}   50: {1,3,3}   51: {2,7}   54: {1,2,2,2}   55: {3,5}   57: {2,8}   60: {1,1,2,3} MATHEMATICA durf[n_]:=Length[Select[Range[PrimeOmega[n]], Reverse[Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]][[#]]>=#&]]; Select[Range[100], durf[#]==2&] CROSSREFS Cf. A006918, A056239, A093641, A112798, A115994, A117485, A252464, A257990, A325163, A325170. Sequence in context: A316752 A110473 A105441 * A093642 A177733 A207675 Adjacent sequences:  A325161 A325162 A325163 * A325165 A325166 A325167 KEYWORD nonn AUTHOR Gus Wiseman, Apr 05 2019 STATUS approved

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Last modified September 18 21:53 EDT 2020. Contains 337173 sequences. (Running on oeis4.)