A325163 Heinz number of the inner lining partition of the integer partition with Heinz number n.

1, 2, 3, 3, 5, 5, 7, 5, 10, 7, 11, 7, 13, 11, 14, 7, 17, 14, 19, 11, 22, 13, 23, 11, 21, 17, 21, 13, 29, 22, 31, 11, 26, 19, 33, 22, 37, 23, 34, 13, 41, 26, 43, 17, 33, 29, 47, 13, 55, 33, 38, 19, 53, 33, 39, 17, 46, 31, 59, 26, 61, 37, 39, 13, 51, 34, 67, 23

Offset

1,2

Comments

The k-th part of the inner lining partition of an integer partition is the number of squares in its Young diagram that are k diagonal steps from the lower-right boundary. 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..68.

Example

The partition with Heinz number 7865 is (6,5,5,3), with diagram
  o o o o o o
  o o o o o
  o o o o o
  o o o
which has diagonal distances
  3 3 3 2 1 1
  3 2 2 2 1
  2 2 1 1 1
  1 1 1
so the inner lining partition is (9,6,4), which has Heinz number 2093, so a(7865) = 2093.

Mathematica

Table[Times@@Prime/@(-Differences[Total/@Take[FixedPointList[If[#=={}, {}, DeleteCases[Rest[#]-1, 0]]&, Reverse[Flatten[Cases[If[n==1, {}, FactorInteger[n]], {p_, k_}:>Table[PrimePi[p], {k}]]]]], {1, -2}]]), {n, 100}]

Crossrefs

Cf. A052126, A056239, A064989, A065770, A093641, A112798, A188674, A252464, A257990, A297113, A325133, A325135, A325164, A325167, A325169.

Sequence in context: A363321 A112823 A247176 * A348538 A185075 A342693

Adjacent sequences: A325160 A325161 A325162 * A325164 A325165 A325166

Keyword

nonn

Author

Gus Wiseman, Apr 05 2019

Status

approved