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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

Table of n, a(n) for n=1..47.

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.)