A391256 Odd semiprimes p*q, such that Stern polynomial B(p*q,x) is a product of B(p,x) and B(q,x).

9, 35, 39, 49, 69, 119, 177, 187, 219, 221, 237, 355, 365, 371, 437, 527, 899, 923, 961, 1257, 1385, 1689, 1691, 2195, 2199, 2285, 2845, 3107, 3133, 3351, 3387, 3403, 3521, 3523, 6881, 7017, 9327, 12319, 14351, 16129, 17555, 17635, 17645, 17817, 18857, 19653, 19689, 22163, 22829, 23315, 23395, 27033, 28739, 32639

Offset

1,1

Links

Antti Karttunen, Table of n, a(n) for n = 1..207

Formula

{odd k such that A001222(k) = 2 and A391239(k) > 2}.

Prog

(PARI) is_A391256(n) = (2==bigomega(n) && is_A391243(n));
(PARI)
memo_for_ps = Map();
ps(n) = if(n<2, n, my(v); if(mapisdefined(memo_for_ps, n, &v), v, v = if(n%2, ps(n\2)+ps(n\2+1), 'x*ps(n\2)); mapput(memo_for_ps, n, v); (v)));
p2r(p) = { my(v=Vecrev(Vec(p))); prod(i=1, #v, prime(i)^v[i]); };
is_A391256(n) = if(!(n%2) || 2!=bigomega(n), 0, my(f=factor(n), a = f[1, 1], b = f[#f~, 1]); (ps(a)*ps(b)) == ps(n));

Crossrefs

Intersection of A046315 and A391243.

Subsequence of A391257.

Cf. A001222, A391239, A391260.

Cf. A133049 (subsequence).

Cf. A125184, A260443 for a description of Stern polynomials.

Cf. also A365473.

Sequence in context: A003865 A265377 A379237 * A187554 A379128 A338010

Adjacent sequences: A391253 A391254 A391255 * A391257 A391258 A391259

Keyword

nonn

Author

Antti Karttunen, Dec 07 2025

Status

approved