A296560 Number of normal semistandard Young tableaux whose shape is the conjugate of the integer partition with Heinz number n.

1, 1, 1, 2, 1, 4, 1, 4, 6, 6, 1, 12, 1, 8, 16, 8, 1, 28, 1, 24, 30, 10, 1, 32, 22, 12, 44, 40, 1, 96, 1, 16, 48, 14, 68, 96, 1, 16, 70, 80, 1, 220, 1, 60, 204, 18, 1, 80, 90, 168, 96, 84, 1, 224, 146, 160, 126, 20, 1, 400, 1, 22, 584, 32, 264, 416, 1, 112, 160

Offset

1,4

Comments

A tableau is normal if its entries span an initial interval of positive integers. 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..69.

Mathematica

a[n_]:=If[n===1, 1, Sum[a[n/q*Times@@Cases[FactorInteger[q], {p_, k_}:>If[p===2, 1, NextPrime[p, -1]^k]]], {q, Rest[Divisors[n]]}]];
Array[a, 100]

Crossrefs

Cf. A000085, A001222, A056239, A063834, A112798, A122111, A138178, A153452, A191714, A210391, A228125, A296150, A296188, A299202.

Sequence in context: A066452 A007104 A102627 * A284652 A261242 A088296

Adjacent sequences: A296557 A296558 A296559 * A296561 A296562 A296563

Keyword

nonn

Author

Gus Wiseman, Feb 15 2018

Status

approved