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A140670
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a(n) is one if n is odd else one less than largest power of two dividing it.
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2
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1, 1, 1, 3, 1, 1, 1, 7, 1, 1, 1, 3, 1, 1, 1, 15, 1, 1, 1, 3, 1, 1, 1, 7, 1, 1, 1, 3, 1, 1, 1, 31, 1, 1, 1, 3, 1, 1, 1, 7, 1, 1, 1, 3, 1, 1, 1, 15, 1, 1, 1, 3, 1, 1, 1, 7, 1, 1, 1, 3, 1, 1, 1, 63, 1, 1, 1, 3, 1, 1, 1, 7, 1, 1, 1, 3, 1, 1, 1, 15, 1, 1, 1, 3, 1, 1, 1, 7, 1, 1, 1, 3, 1, 1, 1, 31, 1, 1, 1, 3, 1, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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FORMULA
| a(n) is multiplicative with a(2^e) = 2^e - 1 if e>0, a(p^e) = 1 if p>2.
a(2*n + 1) = 1. a(-n) = a(n). a(2*n) = 2 * a(n) + (-1)^n unless n=0.
Dirichlet g.f. zeta(s)*(1+2^(1-2s)-2^(1-s))/(1-2^(1-s)). - R. J. Mathar, Feb 07 2011
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PROG
| (PARI) {a(n) = if(n==0, 0, if(n%2, 1, 2^valuation(n, 2) - 1))}
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CROSSREFS
| Sequence in context: A179701 A102480 A157964 * A185587 A068845 A152884
Adjacent sequences: A140667 A140668 A140669 * A140671 A140672 A140673
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KEYWORD
| nonn,mult
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AUTHOR
| Michael Somos, May 21 2008
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