OFFSET
1,1
COMMENTS
Because asymptotically A072213(n) = A000041(n^2) ~ exp(Pi*sqrt(2/3)*n) / (4*sqrt(3)*n^2), the sum of the prime probabilities ~ 1/log(A072213(n)) is diverging and there are no obvious restrictions on primality; therefore, this sequence may be conjectured to be infinite.
Curiously, both A000041(6^2) and A000041(6^4) are prime; in addition, A000041(6^3) and A000041(6^1) are prime, but for no other powers A000041(6^k) is known (or can be expected) to be prime.
a(7) > 649350.
LINKS
Chris K. Caldwell, Top twenty prime partition numbers, The Prime Pages.
Eric Weisstein's World of Mathematics, Partition Function P
Eric Weisstein's World of Mathematics, Integer Sequence Primes
EXAMPLE
a(2) = 6 is in the sequence because A000041(6^2) = 17977 is a prime.
PROG
(PARI) for(n=1, 2500, if(ispseudoprime(numbpart(n^2)), print1(n, ", ")))
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Serge Batalov, Mar 29 2017
STATUS
approved