A227960 Big equivalence classes (A227723) related to subgroups of nimber addition (A190939).

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

Offset: 0

Author

Tilman Piesk, Aug 01 2013

Keywords

• nonn
• tabf

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)

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).

Formula

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

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