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A284594
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Numbers whose square has a prime number of partitions.
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3
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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Table of n, a(n) for n=1..6.
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
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EXAMPLE
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a(2) = 6 is in the sequence because A000041(6^2) = 17977 is a prime.
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PROG
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(PARI) for(n=1, 2500, if(ispseudoprime(numbpart(n^2)), print1(n, ", ")))
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CROSSREFS
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Cf. A000041, A046063, A072213, A285086, A285087, A285088.
Sequence in context: A306793 A326359 A136639 * A027109 A107375 A302863
Adjacent sequences: A284591 A284592 A284593 * A284595 A284596 A284597
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KEYWORD
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nonn,hard,more
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AUTHOR
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Serge Batalov, Mar 29 2017
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STATUS
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approved
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