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 A307410 Numerators of the product in the singular series. 0
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Differs from A305444 at n=35,65,70,... LINKS John Omielan, How do you compute the singular series?. Terence Tao, Correlations of the von Mangoldt and higher divisor functions I. Long shift ranges. See the next formula after equation 2. FORMULA a(n) = numerator of Product_{p|n;p>2}(p-2)/(p-1) where p is a prime number. MAPLE f:= proc(n) numer(mul((p-2)/(p-1), p=select(type, numtheory:-factorset(n), odd))) end proc: map(f, [\$1..100]); # Robert Israel, Apr 07 2019 MATHEMATICA 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[%] PROG (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 CROSSREFS Cf. A005597. Sequence in context: A176801 A339903 A187367 * A305444 A002945 A171232 Adjacent sequences:  A307407 A307408 A307409 * A307411 A307412 A307413 KEYWORD nonn,frac,look AUTHOR Mats Granvik, Apr 07 2019 STATUS approved

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Last modified September 28 19:16 EDT 2021. Contains 347717 sequences. (Running on oeis4.)