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A307410
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Numerators of the product in the singular series.
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0
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1, 1, 1, 1, 3, 1, 5, 1, 1, 3, 9, 1, 11, 5, 3, 1, 15, 1, 17, 3, 5, 9, 21, 1, 3, 11, 1, 5, 27, 3, 29, 1, 9, 15, 5, 1, 35, 17, 11, 3, 39, 5, 41, 9, 3, 21, 45, 1, 5, 3, 15, 11, 51, 1, 27, 5, 17, 27, 57, 3, 59, 29, 5, 1, 11, 9, 65, 15, 21, 5, 69, 1, 71, 35, 3, 17, 3, 11, 77, 3, 1, 39, 81, 5, 45
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OFFSET
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1,5
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COMMENTS
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Differs from A305444 at n=35,65,70,...
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LINKS
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FORMULA
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a(n) = numerator of Product_{p|n;p>2}(p-2)/(p-1) where p is a prime number.
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MAPLE
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f:= proc(n) numer(mul((p-2)/(p-1), p=select(type, numtheory:-factorset(n), odd))) end proc:
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MATHEMATICA
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Table[Times@@(DeleteDuplicates[DeleteCases[DeleteCases[Exp[MangoldtLambda[Divisors[h]]], 1], 2]] - 2)/Times@@(DeleteDuplicates[DeleteCases[DeleteCases[Exp[MangoldtLambda[Divisors[h]]], 1], 2]] - 1), {h, 1, 85}]
Numerator[%]
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PROG
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(PARI) a(n) = my(f=factor(n)[, 1]~); numerator(prod(k=1, #f, if (f[k]>2, (f[k]-2)/(f[k]-1), 1))); \\ Michel Marcus, Apr 07 2019
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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