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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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4
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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COMMENTS
| All numbers occur at least once, but the A000295: Eulerian numbers > 0 appear twice. - (from Robert G. Wilson v (rgwv(at)rgwv.com), Apr 19 2006)
It appears that a(n)=sum{k=0..n-1, (1+(-1)^A000108(k))/2} (n>1). - Paul Barry (pbarry(AT)wit.ie), Mar 31 2008
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REFERENCES
| J. B. Conrey, The Riemann Hypothesis, Notices Amer. Math. Soc., 50 (No. 3, March 2003), 341-353. See p. 347.
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LINKS
| J. B. Conrey, The Riemann Hypothesis
R. Stephan, Some divide-and-conquer sequences ...
R. Stephan, Table of generating functions
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FORMULA
| 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 (ralf(AT)ark.in-berlin.de), Oct 11 2003
Except for a(1), a(n)=n-1-floor(log(2,n)). - (from Robert G. Wilson v (rgwv(at)rgwv.com), Apr 19 2006)
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PROG
| (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
| Cf. A002321. a(n)=n-A070939(n), n>1.
Sequence in context: A172266 A056847 A105598 * A127035 A017876 A017865
Adjacent sequences: A083055 A083056 A083057 * A083059 A083060 A083061
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KEYWORD
| nonn
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AUTHOR
| Michael Somos, Apr 18 2003
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