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A185399
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As p runs through the primes, sequence gives denominator of Sum_{k=1..p-1} 1/k.
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5
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1, 2, 12, 20, 2520, 27720, 720720, 4084080, 5173168, 80313433200, 2329089562800, 13127595717600, 485721041551200, 2844937529085600, 1345655451257488800, 3099044504245996706400, 54749786241679275146400, 3230237388259077233637600
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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) = denominator(sum((k+1)/(p-k-1), k=0..p-2)), where p = the n-th prime. - Gary Detlefs, Jan 12 2012
a(n) = numerator(H(p)/H(p-1)) - denominator(H(p)/H(p-1)), where p is the n-th prime and H(n) is the n-th harmonic number. - Gary Detlefs, Apr 21 2013
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MAPLE
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f2:=proc(n) local p;
p:=ithprime(n);
denom(add(1/i, i=1..p-1));
end proc;
[seq(f2(n), n=1..20)];
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MATHEMATICA
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nn = 20; sm = 0; t = Table[sm = sm + 1/k; Denominator[sm], {k, Prime[nn]}]; Table[t[[p - 1]], {p, Prime[Range[nn]]}] (* T. D. Noe, Apr 23 2013 *)
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PROG
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(PARI) a(n) = denominator(sum(k=1, prime(n)-1, 1/k)); \\ Michel Marcus, Dec 05 2018
(Magma) [Denominator(HarmonicNumber(NthPrime(n)-1)): n in [1..40]]; // Vincenzo Librandi, Dec 05 2018
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CROSSREFS
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Cf. A001008, A002805 (numerators and denominators of harmonic numbers).
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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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