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A227960 Big equivalence classes (A227723) related to subgroups of nimber addition (A190939). 3
1, 3, 6, 15, 24, 60, 105, 255, 384, 960, 1632, 1680, 4080, 15555, 27030, 65535, 98304, 245760, 417792, 430080, 1044480, 1582080, 3947520, 3982080, 6908160, 6919680, 16776960, 106991625, 267448335, 1019462460, 1771476585, 4294967295 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A subsequence of A227723, showing all the big equivalence classes that contain Boolean functions related to subgroups of nimber addition (A190939).

Forms a triangle with row lengths A034343 = 1, 1, 2, 4, 8, 16, 36, 80...:

1,

3,

6, 15,

24, 60, 105, 255,

384, 960, 1632, 1680, 4080, 15555, 27030, 65535...

The left column a( 1,2,4,8,16,32,68,148... ) = a( A076766 ) = 3 ,6, 24, 384, 98304... is probably A001146 * 3/2, which is also A006017( A000079 ).

The first A076766(n) entries correspond to the first A006116(n) entries of A190939. (The first 148 here, for n = 7,  correspond to the first 29212 there.) The entries of A190939 can be generated from this sequence.

Among the first A076766(n) entries are A076831(n;0...n) with weight 2^0...2^n. (Among the first 148 are 1, 7, 23, 43, 43, 23, 7, 1 with weights 1, 2, 4, 8, 16, 32, 64, 128.)

a(n) appears to be divisible by 3 for n>0, and the odd part of a(n) is almost always squarefree. Ralf Stephan, Aug 02 2013

LINKS

Tilman Piesk, Table of n, a(n) for n = 0..147

Tilman Piesk, a(n) for n = 0..147 and corresponding entries of A190939 in reverse binary. Prime factors and numbers of prime factors (A001222).

Tilman Piesk, Subgroups of nimber addition (Wikiversity)

FORMULA

a( A076766 - 1 ) = A001146 - 1 = A051179.

a( A076766 ) = A001146 * 3/2 (probably).

CROSSREFS

Subsequence of A227723 (all becs). All entries are also in A227963 (all sona-secs). Neither shares the property of divisibility by 3.

A190939, A034343, A076766, A076831.

The prime factors contain many prime factors of Fermat numbers (A023394).

Sequence in context: A281212 A062878 A282387 * A282484 A286207 A286502

Adjacent sequences:  A227957 A227958 A227959 * A227961 A227962 A227963

KEYWORD

nonn,tabf

AUTHOR

Tilman Piesk, Aug 01 2013

STATUS

approved

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Last modified December 11 18:34 EST 2019. Contains 329925 sequences. (Running on oeis4.)