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A325180 Heinz number 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 2. 7
5, 8, 10, 12, 20, 21, 35, 36, 42, 49, 54, 60, 63, 70, 81, 84, 90, 98, 100, 105, 126, 135, 140, 147, 150, 189, 196, 210, 225, 275, 294, 315, 385, 441, 500, 539, 550, 605, 700, 750, 770, 825, 847, 980, 1050, 1078, 1100, 1125, 1155, 1210, 1250, 1331, 1372, 1375 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The enumeration of these partitions by sum is given by A325182.

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..54.

Gus Wiseman, Young diagrams corresponding to the first 96 terms.

EXAMPLE

The sequence of terms together with their prime indices begins:

    5: {3}

    8: {1,1,1}

   10: {1,3}

   12: {1,1,2}

   20: {1,1,3}

   21: {2,4}

   35: {3,4}

   36: {1,1,2,2}

   42: {1,2,4}

   49: {4,4}

   54: {1,2,2,2}

   60: {1,1,2,3}

   63: {2,2,4}

   70: {1,3,4}

   81: {2,2,2,2}

   84: {1,1,2,4}

   90: {1,2,2,3}

   98: {1,4,4}

  100: {1,1,3,3}

  105: {2,3,4}

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[#]==2&]

CROSSREFS

Numbers k such that A263297(k) - A257990(k) = 2.

Positions of 2's in A325178.

Cf. A006918, A056239, A093641, A112798, A325164, A325170, A325179, A325182, A325192, A325197.

Sequence in context: A314380 A332513 A314381 * A087280 A335495 A280537

Adjacent sequences:  A325177 A325178 A325179 * A325181 A325182 A325183

KEYWORD

nonn

AUTHOR

Gus Wiseman, Apr 08 2019

STATUS

approved

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Last modified October 29 21:18 EDT 2020. Contains 338074 sequences. (Running on oeis4.)