A389912 - OEIS

%I #18 Dec 03 2025 21:50:53

%S 3,6,18,30,270,450,630,2310,6750,9450,15750,22050,90090,510510,727650,

%T 2668050,3543750,4961250,18191250,25467750,29099070

%N Prime-factorization representation of irreducible (non-constant) Stern-polynomials B(m,x), listed in ascending order.

%C See A260443 for how Stern-polynomials can be encoded with the prime factorization of natural numbers.

%C Numbers k > 2 such that A277333(k) is in A186891.

%H Maciej Ulas and Oliwia Ulas, <a href="https://arxiv.org/abs/1102.5109">On certain arithmetic properties of Stern polynomials</a>, arXiv:1102.5109 [math.CO], 2011. (See Conjecture 6.4. on p. 20)

%F {k such that A389449(k)*A389911(k) = 1}.

%F {k such that A389449(k)*A389913(k) = 1}.

%o (PARI) is_A389912(n) = (A389449(n) && A389911(n));

%o (PARI) is_A389912(n) = { my(k); if(3==n, 1, if(n%2 || (omega(n) < A061395(n)), 0, k = A048675(n); if((A260443(k) == n), A283991(k), 0))); };

%Y Sequence A277318 sorted into ascending order.

%Y Intersection of A206284 and A260442.

%Y Intersection of A260442 and A389914.

%Y After the initial 3, subsequence of A055932.

%Y Cf. A186891, A260443, A277317 (conjectured subsequence), A277333, A283991, A389449, A389911, A389913.

%K nonn,more

%O 1,1

%A _Antti Karttunen_, Dec 03 2025