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

%I A227960 #39 Mar 18 2020 06:53:14
%S A227960 1,3,6,15,24,60,105,255,384,960,1632,1680,4080,15555,27030,65535,
%T A227960 98304,245760,417792,430080,1044480,1582080,3947520,3982080,6908160,
%U A227960 6919680,16776960,106991625,267448335,1019462460,1771476585,4294967295
%N A227960 Big equivalence classes (A227723) related to subgroups of nimber addition (A190939).
%C A227960 A subsequence of A227723, showing all the big equivalence classes that contain Boolean functions related to subgroups of nimber addition (A190939).
%C A227960 Forms a triangle with row lengths A034343 = 1, 1, 2, 4, 8, 16, 36, 80...:
%C A227960 1,
%C A227960 3,
%C A227960 6, 15,
%C A227960 24, 60, 105, 255,
%C A227960 384, 960, 1632, 1680, 4080, 15555, 27030, 65535...
%C A227960 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 ).
%C A227960 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.
%C A227960 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.)
%C A227960 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
%H A227960 Tilman Piesk, <a href="/A227960/b227960.txt">Table of n, a(n) for n = 0..147</a>
%H A227960 Tilman Piesk, <a href="/A227960/a227960.txt">a(n) for n = 0..147</a> and <a href="/A227960/a227960_1.txt">corresponding entries</a> of A190939 in reverse binary. <a href="http://pastebin.com/raw.php?i=t8eFAVZi">Prime factors</a> and <a href="http://pastebin.com/raw.php?i=UHiiaxkC">numbers of prime factors</a> (A001222).
%H A227960 Tilman Piesk, <a href="http://en.wikiversity.org/wiki/Subgroups_of_nimber_addition">Subgroups of nimber addition</a> (Wikiversity)
%F A227960 a( A076766 - 1 ) = A001146 - 1 = A051179.
%F A227960 a( A076766 ) = A001146 * 3/2 (probably).
%Y A227960 Subsequence of A227723 (all becs). All entries are also in A227963 (all sona-secs). Neither shares the property of divisibility by 3.
%Y A227960 A190939, A034343, A076766, A076831.
%Y A227960 The prime factors contain many prime factors of Fermat numbers (A023394).
%K A227960 nonn,tabf
%O A227960 0,2
%A A227960 _Tilman Piesk_, Aug 01 2013