cp's OEIS Frontend

A345225 a(n) = order of 2-primary subgroup of the group K_n(Z).

%I A345225 #28 Jun 13 2021 03:18:02
%S A345225 1,2,2,16,1,1,1,16,1,2,2,16,1,1,1,32,1,2,2,16,1,1,1,48,1,2,2,16,1,1,1,
%T A345225 64,1,2,2,16,1,1,1,80,1,2,2,16,1,1,1,96,1,2,2,16,1,1,1,112,1,2,2,16,1,
%U A345225 1,1,128,1,2,2,16,1,1,1,144,1,2,2,16,1,1,1,160
%N A345225 a(n) = order of 2-primary subgroup of the group K_n(Z).
%C A345225 The algebraic K-theory groups of the integers are not yet (as of June 2021) completely known, however the 2-primary part is settled.
%C A345225 In fact, the 2-primary part of the abelian group K_n(Z) is the cyclic group Z/a(n)Z.
%D A345225 C. Weibel, The K-book: An Introduction to Algebraic K-theory. Graduate Studies in Mathematics, 145. American Mathematical Society, Providence, RI, 2013. ISBN: 978-0-8218-9132-.
%H A345225 Tom Harris, <a href="/A345225/b345225.txt">Table of n, a(n) for n = 0..9999</a>
%H A345225 C. Weibel, <a href="https://doi.org/10.1016/S0764-4442(97)86977-7">The 2-torsion in the K-theory of the integers</a>, C. R. Acad. Sci. Paris 324 (1997), 615-620.
%F A345225 a(n) is:
%F A345225         1 if n mod 8 = 0, 4, 5, or 6
%F A345225         2 if n mod 8 = 1 or 2
%F A345225        16 if n mod 8 = 3
%F A345225   2*(n+1) if n mod 8 = 7.
%F A345225 (The main result of Weibel's 1997 paper on the 2-torsion in the K-theory of the integers; Corollary 9.8 of Weibel's K-book.)
%o A345225 (Python)
%o A345225 def a(n):
%o A345225     n_ = (n % 8)
%o A345225     d = {0:1, 1:2, 2:2, 3:16, 4:1, 5:1, 6:1}
%o A345225     if n_ == 7:
%o A345225         return 2*(n+1)
%o A345225     else:
%o A345225         return d[n_]
%K A345225 easy,nonn
%O A345225 0,2
%A A345225 _Tom Harris_, Jun 11 2021