Search: id:A068067
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%I A068067
%S A068067 1,0,2,0,2,1,2,0,2,1,2,1,2,1,4,0,2,1,2,1,4,1,2,1,2,1,2,1,2,3,2,0,4,1,4,
%T A068067 1,2,1,4,1,2,3,2,1,4,1,2,1,2,1,4,1,2,1,4,1,4,1,2,3,2,1,4,0,4,3,2,1,4,3,
%U A068067 2,1,2,1,4,1,4,3,2,1,2,1,2,3,4,1,4,1,2,3,4,1,4,1,4,1,2,1,4,1,2,3,2,1,8
%N A068067 Number of integers m, 0 < m <= n, such that n divides m(m+1)/2.
%C A068067 a(n) = 0 iff n = 2^k with k >= 1.
%C A068067 Least n with a(n) = 2^k is p(k+1)#/2 = A002110(A000040(k+1))/2. Least 
               n with a(n) = 2^k-1 != 1 is p(k+1)#.
%F A068067 If n is even, a(n) = 2^(omega(n)-1) - 1; if n is odd, a(n) = 2^omega(n). 
               Here omega(n) = A001221(n) is the number of distinct prime divisors 
               of n.
%t A068067 a[n_] := Length[Select[Range[n], Mod[ #(#+1)/2, n]==0&]]
%Y A068067 Cf. A068068(n)-a(n) = 0 if n is odd, 1 if n is even.
%Y A068067 Sequence in context: A068907 A033687 A133457 this_sequence A046926 A074398 
               A144765
%Y A068067 Adjacent sequences: A068064 A068065 A068066 this_sequence A068068 A068069 
               A068070
%K A068067 nonn
%O A068067 1,3
%A A068067 Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 18 2002
%E A068067 Edited by David W. Wilson (davidwwilson(AT)comcast.net) and Dean Hickerson 
               (dean.hickerson(AT)yahoo.com), Jun 08 2002

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