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A267092
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a(n) is the number of P-positions for n-modular Nim with 2 piles.
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2
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1, 3, 3, 8, 5, 9, 7, 20, 9, 15, 11, 24, 13, 21, 15, 48, 17, 27, 19, 40, 21, 33, 23, 60, 25, 39, 27, 56, 29, 45, 31, 112, 33, 51, 35, 72, 37, 57, 39, 100, 41, 63, 43, 88, 45, 69, 47, 144, 49, 75, 51, 104, 53, 81, 55, 140, 57, 87, 59, 120, 61, 93, 63, 256, 65, 99, 67, 136
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OFFSET
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1,2
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COMMENTS
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The sequence is multiplicative.
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LINKS
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FORMULA
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a(n) = n, if n is odd.
a(2*n) = n + 2*a(n).
a(n) = n(nu(n)/2+1), where nu(n) is the 2-adic order of n.
Multiplicative with a(2^e)=(e+2)*2^(e-1) and a(p^e)=p^e for p>2 and e>0.
Dirichlet g.f.: zeta(s-1)*(2^s-1)/(2^s-2).
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EXAMPLE
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The P-positions for 2-modular Nim with 2 piles are: (0,0), (1,2), (2,1). Thus a(2) = 3.
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MATHEMATICA
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Table[n (IntegerExponent[n, 2]/2 + 1), {n, 100}]
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PROG
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(PARI) a(n) = n*(valuation(n, 2)/2 + 1); \\ Michel Marcus, Jan 13 2016
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CROSSREFS
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KEYWORD
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nonn,mult,easy
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AUTHOR
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STATUS
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approved
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