A350069 Semiprimes k such that 1+(2^(1+A243055(k))) is a Fermat prime, where A243055(k) gives the difference between the indices of the smallest and the largest prime divisor of k.

4, 6, 9, 14, 15, 25, 33, 35, 38, 49, 65, 69, 77, 106, 119, 121, 143, 145, 169, 177, 209, 217, 221, 289, 299, 305, 323, 361, 407, 437, 469, 493, 529, 533, 589, 667, 731, 781, 841, 851, 893, 899, 949, 961, 1147, 1189, 1219, 1333, 1343, 1369, 1517, 1577, 1681, 1711, 1739, 1763, 1849, 1891, 2021, 2047, 2173, 2209, 2479

Offset: 1

Author

Antti Karttunen, Jan 29 2022

Keywords

• nonn

Examples

			9 is a semiprime (9 = 3*3), and as the difference between the indices of the smallest (3) and the largest prime (3) dividing 9 is 0, we have 1+(2^(1+A243055(k))) = 3, which is in A019434, and therefore 9 is included in this sequence, like all squares of primes (A001248).
177 = 3 * 59 = prime(2) * prime(17), therefore A243055(177) = 17-2 = 15, and as 1+(2^16) = 65537 is also in A019434, 177 is included in this sequence.
		

Links

• Index entries for sequences computed from indices in prime factorization

Crossrefs

Positions of ones in A342651.

Cf. A019434, A209229, A243055, A334101.

Subsequence of A001358. A001248 is a subsequence.

Programs

PARI

A209229(n) = (n && !bitand(n,n-1));
A243055(n) = if(1==n,0,my(f = factor(n), lpf = f[1, 1], gpf = f[#f~, 1]); (primepi(gpf)-primepi(lpf)));
isA350069(n) = if(2!=bigomega(n),0,my(d=1+A243055(n)); (A209229(d) && isprime(1+(2^d))));