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

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, 36, 37, 38, 39, 41, 42, 44, 47, 48, 49, 50, 52, 54, 55, 56, 57, 59, 61, 62, 63, 64, 66, 67, 72, 73, 74, 75, 76, 77, 78, 81, 82, 84, 87, 88, 91, 93, 94, 96, 97, 98, 99, 100, 103

Offset: 1

Author

Antti Karttunen, Jan 31 2014

Keywords

• nonn

Comments

This sequence gives the range of A234742.

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.

Above condition implies that none of the terms of A091209 occur here.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..13487

Crossrefs

Complement: A236844. A236860 is a subsequence.

Positions of nonzero terms in A236853.

Cf. A234742, A236841.

Formula

Use the characteristic function A236862(n) to determine whether n is a term of this sequence or not.

Specifically:

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.

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

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