A317299 Semiprimes in A072226.

4, 6, 9, 10, 14, 15, 22, 26, 33, 34, 38, 46, 49, 62, 65, 69, 77, 85, 86, 93, 122, 129, 133, 145, 158, 202, 254, 334, 382, 398, 447, 471, 579, 626, 694, 745, 1402, 1727, 1781, 2353, 3415, 3418, 3481, 3817, 5053, 5234, 5403, 7078, 7617, 8033, 10967, 11581

Offset: 1

Author

Jianing Song, Jan 22 2019

Keywords

• nonn

Comments

Semiprimes k such that A019320(k) is prime.

Numbers of the form p^2 where (2^(p^2) - 1)/(2^p - 1) is prime, or numbers of the form p*q where (2^(p*q) - 1)/((2^p - 1)*(2^q - 1)) is prime. Here p and q are necessarily primes.

Examples

			15 is a semiprime and Phi_15(2) = (2^15 - 1)/((2^3 - 1)*(2^5 - 1)) = 151 is prime, so 15 is a term. Here Phi_n is the n-th cyclotomic polynomial.
49 is a semiprime and Phi_49(2) = (2^49 - 1)/(2^7 - 1) = 4432676798593 is prime, so 49 is a term.
		

Links

• Jianing Song and Max Alekseyev, Table of n, a(n) for n = 1..79 (using data from A072226)

Crossrefs

Cf. A019320, A072226.

Programs

PARI

for(k=1, 1000, if(isprime(polcyclo(k, 2))&&bigomega(k)==2,print1(k, ", ")))