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 A307515 Heinz numbers of integer partitions with Durfee square of length > 2. 2
 125, 175, 245, 250, 275, 325, 343, 350, 375, 385, 425, 455, 475, 490, 500, 525, 539, 550, 575, 595, 605, 625, 637, 650, 665, 686, 700, 715, 725, 735, 750, 770, 775, 805, 825, 833, 845, 847, 850, 875, 910, 925, 931, 935, 950, 975, 980, 1000, 1001, 1015, 1025 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS First differs from A307386 in having 7^4 = 2401. 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. The enumeration of these partitions by sum is given by A084835. REFERENCES Richard P. Stanley, Enumerative Combinatorics, Volume 2,  Cambridge University Press, 1999, p. 289. LINKS Gus Wiseman, Table of n, a(n) for n = 1..22485 Wikipedia, Durfee square. 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[#]>2&] CROSSREFS Positions of numbers > 2 in A257990. Cf. A006918, A056239, A084835, A112798, A115994, A117485, A252464, A325163, A325170. Sequence in context: A069656 A196943 A307386 * A038513 A251125 A252065 Adjacent sequences:  A307512 A307513 A307514 * A307516 A307517 A307518 KEYWORD nonn AUTHOR Gus Wiseman, Apr 12 2019 STATUS approved

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Last modified September 24 22:28 EDT 2020. Contains 337325 sequences. (Running on oeis4.)