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A056190
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a(n) = Sum_{d|n and gcd(d, n/d)=1} binomial(n,d).
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1
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1, 3, 4, 5, 6, 42, 8, 9, 10, 308, 12, 728, 14, 3538, 3474, 17, 18, 48792, 20, 20370, 117632, 705686, 24, 737520, 26, 10400952, 28, 1204544, 30, 185903342, 32, 33, 193542210, 2333606816, 7049188, 94202222, 38, 35345264542, 8122434623
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = A056045(n) for squarefree n, when all divisors are unitary.
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EXAMPLE
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n=100 has 9 divisors of which {1,4,25,100} are unitary, so a(100) = 100 + 3921225 + 242519269720337121015504 + 1.
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MAPLE
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a:= n-> add(`if`(igcd(d, n/d)=1, binomial(n, d), 0),
d=numtheory[divisors](n)):
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PROG
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(PARI) a(n) = sumdiv(n, d, if (gcd(d, n/d)==1, binomial(n, d))); \\ Michel Marcus, Aug 25 2019
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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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