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A083058
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Number of eigenvalues equal to 1 of n X n matrix A(i,j)=1 if j=1 or i divides j.
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8
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1, 0, 1, 1, 2, 3, 4, 4, 5, 6, 7, 8, 9, 10, 11, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66
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OFFSET
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1,5
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COMMENTS
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It appears that a(n) = Sum_{k=0..n-1} (1 + (-1)^A000108(k))/2 (n > 1). - Paul Barry, Mar 31 2008
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LINKS
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FORMULA
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a(1)=1, else a(n)=b(n) with b(0)=0, b(2n)=b(n)+n-1, b(2n+1)=b(n)+n. - Ralf Stephan, Oct 11 2003
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MAPLE
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if n = 1 then
1;
else
n-floor(log[2](n))-1 ;
end if;
end proc:
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MATHEMATICA
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a[1] = 1; a[n_] := n - Floor[Log[2, n]] - 1;
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PROG
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(PARI) a(n)=if(n<2, n>0, n-floor(log(n)/log(2))-1)
(PARI) a(n)= if(n<1, 0, valuation( subst( charpoly( matrix(n, n, i, j, (j==1) || (0==j%i))), x, x+1), x))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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