The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A308542 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A308542

Number of subsets of {2..n} containing the product of any set of distinct elements whose product is <= n.
(history; published version)

#8 by N. J. A. Sloane at Sun Aug 25 19:44:03 EDT 2019

STATUS

proposed

approved

#7 by Andrew Howroyd at Sun Aug 25 17:30:17 EDT 2019

STATUS

editing

proposed

#6 by Andrew Howroyd at Sat Aug 24 15:36:29 EDT 2019

DATA

1, 2, 4, 8, 16, 28, 56, 100, 200, 364, 728, 1184, 2368, 4448, 8056, 15008, 30016, 52736, 105472, 183424, 339840, 663616, 1327232, 2217088, 4434176, 8744320, 16559168, 30034624, 60069248, 103402112, 206804224, 379941440, 730800064, 1454649248, 2659869664, 4786282208

KEYWORD

nonn,more

nonn

EXTENSIONS

Terms a(21) and beyond from Andrew Howroyd, Aug 24 2019

STATUS

approved

editing

#5 by Susanna Cuyler at Thu Jun 06 21:57:37 EDT 2019

STATUS

proposed

approved

#4 by Gus Wiseman at Thu Jun 06 21:47:19 EDT 2019

STATUS

editing

proposed

#3 by Gus Wiseman at Thu Jun 06 17:17:58 EDT 2019

NAME

allocated for Gus WisemanNumber of subsets of {2..n} containing the product of any set of distinct elements whose product is <= n.

DATA

1, 2, 4, 8, 16, 28, 56, 100, 200, 364, 728, 1184, 2368, 4448, 8056, 15008, 30016, 52736, 105472, 183424

OFFSET

1,2

COMMENTS

First differs from A326116 at a(12) = 1184, A326116(12) = 1232.

If this sequence counts product-closed sets, A326116 counts product-free sets.

FORMULA

For n > 0, a(n) = A326081(n)/2.

EXAMPLE

The a(6) = 28 sets:

{} {2} {2,4} {2,3,6} {2,3,4,6} {2,3,4,5,6}

{3} {2,5} {2,4,5} {2,3,5,6}

{4} {2,6} {2,4,6} {2,4,5,6}

{5} {3,4} {2,5,6} {3,4,5,6}

{6} {3,5} {3,4,5}

{3,6} {3,4,6}

{4,5} {3,5,6}

{4,6} {4,5,6}

{5,6}

MATHEMATICA

Table[Length[Select[Subsets[Range[2, n]], SubsetQ[#, Select[Times@@@Subsets[#, {2}], #<=n&]]&]], {n, 0, 10}]

CROSSREFS

Cf. A007865, A051026, A103580, A196724, A326020, A326023, A326076, A326078, A326079, A326081, A326116, A326117.

KEYWORD

allocated

nonn,more

AUTHOR

Gus Wiseman, Jun 06 2019

STATUS

approved

editing

#2 by Gus Wiseman at Thu Jun 06 17:07:05 EDT 2019

NAME

allocated for Gus Wiseman

KEYWORD

recycled

allocated

#1 by Russ Cox at Sun Jan 27 08:30:53 EST 2019

KEYWORD

recycled

STATUS

approved