A368297 Prime plane partition numbers.

3, 13, 859, 5668963, 12733429, 281846923, 10499640707, 776633557947931, 59206066030052023, 13621664240071959464038764694637, 27217095019687611064080107410267607999874139, 208912772327685894433117242327777497768893400876928857463950152067659

Offset: 1

Author

Ilya Gutkovskiy, Dec 20 2023

Keywords

• nonn

Comments

Prime values of A000219.

Links

• Eric Weisstein's World of Mathematics, Plane Partition

Crossrefs

Cf. A000219, A049575, A051005, A285216 (indices).

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(
      a(n-j)*numtheory[sigma][2](j), j=1..n)/n)
    end:
select(isprime, [seq(a(n), n=0..800)])[];  # Alois P. Heinz, Dec 20 2023

Mathematica

nmax = 750; Select[CoefficientList[Series[Product[1/(1 - x^k)^k, {k, 1, nmax}], {x, 0, nmax}], x], PrimeQ]

Formula

a(n) = A000219(A285216(n)).