A377045 Number of partitions of cuban primes.

15, 490, 21637, 1121505, 3913864295, 1131238503938606, 78801255302666615, 5589233202595404488, 29349508915133986374841, 2163909235608484556362424, 913865816485680423486405066750, 191623400974625892978847721669762887224010

Offset: 1

Author

Paul F. Marrero Romero, Oct 14 2024

Keywords

• nonn

Comments

Number of partitions of prime numbers that are the difference of two consecutive cubes.

Number of partitions of primes p such that p=(3*k^2 + 1)/4 for some integer k (A121259).

Links

• Robert Israel, Table of n, a(n) for n = 1..153

Crossrefs

Cf. A000041, A002407, A121259.

Programs

Maple

R:= NULL: count:= 0:
for i from 1 while count < 30 do
  p:= (i+1)^3 - i^3;
  if isprime(p) then count:= count+1; v:= combinat:-numbpart(p); R:= R,v; fi
od:
R; # Robert Israel, Nov 14 2024

Mathematica

PartitionsP[Select[Table[(3k^2 + 1)/4,{k,50}],PrimeQ]]

Formula

a(n) = A000041(A002407(n)).

a(n) = A000041((3*A121259(n)^2 + 1)/4).