cp's OEIS Frontend

A236842 Numbers that occur as results of remultiplication (GF(2)[X] -> N) of some number; A234742 sorted and duplicates removed.

%I A236842 #38 Mar 10 2014 08:26:57
%S A236842 0,1,2,3,4,6,7,8,9,11,12,13,14,16,18,19,21,22,24,25,26,27,28,31,32,33,
%T A236842 36,37,38,39,41,42,44,47,48,49,50,52,54,55,56,57,59,61,62,63,64,66,67,
%U A236842 72,73,74,75,76,77,78,81,82,84,87,88,91,93,94,96,97,98,99,100,103
%N A236842 Numbers that occur as results of remultiplication (GF(2)[X] -> N) of some number; A234742 sorted and duplicates removed.
%C A236842 This sequence gives the range of A234742.
%C A236842 After 0 and 1 these are numbers n that have such a multiset of prime divisors p, q, ..., w (p * q * ... * w = n, with p, q, ..., w not necessarily distinct) that it can be arranged so that in at least one subset of divisors of n: (p, q, w), (pq, w), (pw, q), (p, qw), (pqw), ..., all divisors (for example, in the second case: pq and w) encode by their binary representations irreducible factors of polynomial ring over GF(2) (i.e., all occur in A014580) and their (ordinary) product is n.
%C A236842 Above condition implies that none of the terms of A091209 occur here.
%H A236842 Antti Karttunen, <a href="/A236842/b236842.txt">Table of n, a(n) for n = 1..13487</a>
%F A236842 Use the characteristic function A236862(n) to determine whether n is a term of this sequence or not.
%F A236842 Specifically:
%F A236842 All numbers encoding an irreducible polynomial in GF(2)[X] (A014580) occur in this sequence. This means that a prime is in this sequence if and only if it is in A091206.
%F A236842 On the other hand, a composite integer n is in this sequence if and only if it is either in A014580 or it has such a proper factor k (1<k<n, k|n) that both k and n/k are members of this sequence.
%o A236842 (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o A236842 (define A236842 (NONZERO-POS 1 0 A236862))
%o A236842 (define A236842 (NONZERO-POS 1 0 A236853))
%Y A236842 Complement: A236844. A236860 is a subsequence.
%Y A236842 Positions of nonzero terms in A236853.
%Y A236842 Cf. A234742, A236841.
%K A236842 nonn
%O A236842 1,3
%A A236842 _Antti Karttunen_, Jan 31 2014