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A260502 Log_2 of the numerator of det(M) where M is the n X n matrix with M[i,j] = 1/lcm(i,j).

%I A260502 #64 Aug 24 2015 17:30:49
%S A260502 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%T A260502 1,0,1,0,3,1,4,4,5,3,6,5,6,2,3,3,8,7,9,8,11,8,10,10,11,11,13,12,14,7,
%U A260502 11,11,12,13,15,16,17,14,17,17,20,18,20,21,22,19,20,21,22,21,27,26,29,26,29
%N A260502 Log_2 of the numerator of det(M) where M is the n X n matrix with M[i,j] = 1/lcm(i,j).
%C A260502 Powers of two not present in A260897: 23, 24, 25, 28, 38, 46, 47, 49, 55, 63, 64, 69, ..., .
%H A260502 Robert G. Wilson v, <a href="/A260502/b260502.txt">Table of n, a(n) for n = 1..500</a>
%F A260502 a(n) = A007814(A260897(n)).
%e A260502 a(4) = 0 because for n=4 det(M) = 1/144.
%e A260502 a(35) = 1 because for n=35 det(M) equals 2/5029296746186844716050163189085401314000634765625.
%t A260502 f[n_] := Log2@ Numerator@ Det@ Table[ 1/LCM[i, j], {i, n}, {j, n}]; Array[f, 85]
%o A260502 (PARI) vector(80, n, valuation(denominator(1/matdet(matrix(n, n, i, j, 1/lcm(i, j)))), 2)) \\ _Michel Marcus_, Aug 04 2015
%Y A260502 Cf. A060841, A007814, A260897.
%K A260502 nonn
%O A260502 1,39
%A A260502 _Robert G. Wilson v_, Aug 02 2015