A368297 - OEIS

%I #13 Dec 21 2023 10:23:14

%S 3,13,859,5668963,12733429,281846923,10499640707,776633557947931,

%T 59206066030052023,13621664240071959464038764694637,

%U 27217095019687611064080107410267607999874139,208912772327685894433117242327777497768893400876928857463950152067659

%N Prime plane partition numbers.

%C Prime values of A000219.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PlanePartition.html">Plane Partition</a>

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

%p a:= proc(n) option remember; `if`(n=0, 1, add(

%p       a(n-j)*numtheory[sigma][2](j), j=1..n)/n)

%p     end:

%p select(isprime, [seq(a(n), n=0..800)])[];  # _Alois P. Heinz_, Dec 20 2023

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

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

%K nonn

%O 1,1

%A _Ilya Gutkovskiy_, Dec 20 2023