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 A325179 Heinz numbers of integer partitions such that the difference between the length of the minimal square containing and the maximal square contained in the Young diagram is 1. 7
 3, 4, 6, 15, 18, 25, 27, 30, 45, 50, 75, 175, 245, 250, 343, 350, 375, 490, 525, 625, 686, 735, 875, 1029, 1225, 1715, 3773, 4802, 5929, 7203, 7546, 9317, 11319, 11858, 12005, 14641, 16807, 17787, 18634, 18865, 26411, 27951, 29282, 29645, 41503, 43923, 46585 (list; graph; refs; listen; history; text; internal format)
 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 Gus Wiseman, Young diagrams for the first 32 terms. 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 Numbers k such that A263297(k) - A257990(k) = 1. Positions of 1's in A325178. Cf. A056239, A093641, A112798, A325180, A325181, A325192, A325196, A325198. Sequence in context: A063477 A168219 A129827 * A308533 A322956 A122727 Adjacent sequences:  A325176 A325177 A325178 * A325180 A325181 A325182 KEYWORD nonn AUTHOR Gus Wiseman, Apr 08 2019 STATUS approved

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Last modified November 25 14:47 EST 2020. Contains 338625 sequences. (Running on oeis4.)