A123664 - OEIS

A123664

a(1) = 1, a(2) = 2; then all new products of subsets of pre-existing terms which include the most recent, then the first integer not present and so on.

1, 2, 3, 6, 4, 8, 12, 24, 48, 72, 144, 5, 10, 15, 20, 30, 40, 60, 80, 90, 120, 160, 180, 240, 320, 360, 480, 720, 960, 1080, 1440, 1920, 2160, 2880, 3840, 4320, 5760, 6480, 7680, 8640, 11520, 12960, 15360, 17280, 23040, 25920, 34560, 46080, 51840, 69120, 77760

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OFFSET

1,2

COMMENTS

Similar to A096113. However, each product must include the most recently added singleton. Thus after adding 4, the terms 18 and 36 are not added because they have no representation as a product of earlier terms, including 4. A110797 is similar, but only allows products of pairs (not of subsets).

LINKS

Table of n, a(n) for n=1..51.

EXAMPLE

After a(1) = 1, a(2) = 2, all products are present, so we add the first integer not included, namely 3. Then we add all products of any subset of {1, 2, 3} which include 3 and are not already present, in this case just 6. Then we add the next integer not already present, 4. Then we add all products of any subset of {1, 2, 3, 6, 4} which include 4 and are not already present, 8 (=2*4), 12 (=3*4), 24 (=2*3*4=6*4), 48 (=2*6*4), 72 (=3*6*4) and 144 (=2*3*6*4). Then we add 5, the next integer not already present. And so on.

MATHEMATICA

M[2]={1, 2} M[n_]:= Join[M[n-1], Complement[Union[M[n-1][[ -1]] * Exp[Map[Total, Log[Subsets[Delete[Delete[M[n-1], 1], -1]]]]]], M[n-1]], {n}] M[6]

CROSSREFS

Cf. A096113.

Sequence in context: A052330 A344535 A059900 * A084980 A101369 A125147

Adjacent sequences: A123661 A123662 A123663 * A123665 A123666 A123667

KEYWORD

nonn

AUTHOR

Joel B. Lewis, Nov 15 2006

STATUS

approved