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%I #16 May 05 2019 11:59:15
%S 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,
%T 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,
%U 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
%N Numerators of the product in the singular series.
%C Differs from A305444 at n=35,65,70,...
%H John Omielan, <a href="https://math.stackexchange.com/a/3178061/8530">How do you compute the singular series?</a>.
%H Terence Tao, <a href="https://terrytao.wordpress.com/2017/07/06/correlations-of-the-von-mangoldt-and-higher-divisor-functions-i-long-shift-ranges/">Correlations of the von Mangoldt and higher divisor functions I. Long shift ranges</a>. See the next formula after equation 2.
%F a(n) = numerator of Product_{p|n;p>2}(p-2)/(p-1) where p is a prime number.
%p f:= proc(n) numer(mul((p-2)/(p-1),p=select(type,numtheory:-factorset(n),odd))) end proc:
%p map(f, [$1..100]); # _Robert Israel_, Apr 07 2019
%t 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}]
%t Numerator[%]
%o (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
%Y Cf. A005597.
%K nonn,frac,look
%O 1,5
%A _Mats Granvik_, Apr 07 2019
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