This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A317299 #33 Dec 04 2024 10:14:06 %S A317299 4,6,9,10,14,15,22,26,33,34,38,46,49,62,65,69,77,85,86,93,122,129,133, %T A317299 145,158,202,254,334,382,398,447,471,579,626,694,745,1402,1727,1781, %U A317299 2353,3415,3418,3481,3817,5053,5234,5403,7078,7617,8033,10967,11581 %N A317299 Semiprimes in A072226. %C A317299 Semiprimes k such that A019320(k) is prime. %C A317299 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. %H A317299 Jianing Song and Max Alekseyev, <a href="/A317299/b317299.txt">Table of n, a(n) for n = 1..79</a> (using data from A072226) %e A317299 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. %e A317299 49 is a semiprime and Phi_49(2) = (2^49 - 1)/(2^7 - 1) = 4432676798593 is prime, so 49 is a term. %o A317299 (PARI) for(k=1, 1000, if(isprime(polcyclo(k, 2))&&bigomega(k)==2,print1(k, ", "))) %Y A317299 Cf. A019320, A072226. %K A317299 nonn %O A317299 1,1 %A A317299 _Jianing Song_, Jan 22 2019