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A178101
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Cardinality of the set of d, 2<=d<=n/2, which divide binomial(n-d-1,d-1) and are not coprime to n.
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8
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 1, 1, 0, 2, 0, 3, 0, 4, 0, 2, 0, 3, 1, 2, 0, 2, 0, 2, 3, 5, 0, 5, 0, 6, 3, 3, 0, 6, 1, 3, 3, 8, 0, 5, 0, 11, 3, 8, 1, 8, 0, 5, 3, 7, 0, 6, 0, 8, 4, 5, 1, 7, 0, 7, 5, 10, 0, 4, 1, 9, 3, 6, 0, 10, 2, 8, 4, 15, 2, 10, 0, 16, 6, 10
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OFFSET
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1,26
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COMMENTS
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Note that every d>1 divides binomial(n-d-1,d-1), if gcd(n,d)=1.
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LINKS
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MAPLE
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A178101 := proc(n) local dvs, d ; dvs := {} ; for d from 1 to n/2 do if gcd(n, d) > 1 and d in numtheory[divisors]( binomial(n-d-1, d-1)) then dvs := dvs union {d} ; end if; end do: nops(dvs) end proc: # R. J. Mathar, May 28 2010
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MATHEMATICA
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a[n_] := Sum[Boole[Divisible[Binomial[n-d-1, d-1], d] && !CoprimeQ[d, n]], {d, 2, n/2}];
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PROG
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(PARI) a(n) = sum(d=2, n\2, (gcd(d, n) != 1) && ((binomial(n-d-1, d-1) % d) == 0)); \\ Michel Marcus, Feb 17 2016
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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a(54), a(68), a(70), a(72), a(78) etc corrected by R. J. Mathar, May 28 2010
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STATUS
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approved
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