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.

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

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 A355569

Adjacent sequences: A325177 A325178 A325179 * A325181 A325182 A325183

Keyword

nonn

Author

Gus Wiseman, Apr 08 2019

Status

approved