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A185399 As p runs through the primes, sequence gives denominator of Sum_{k=1..p-1} 1/k.

%I A185399 #36 Mar 29 2025 15:31:16
%S A185399 1,2,12,20,2520,27720,720720,4084080,5173168,80313433200,
%T A185399 2329089562800,13127595717600,485721041551200,2844937529085600,
%U A185399 1345655451257488800,3099044504245996706400,54749786241679275146400,3230237388259077233637600
%N A185399 As p runs through the primes, sequence gives denominator of Sum_{k=1..p-1} 1/k.
%D A185399 Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See pp. 22-23.
%H A185399 T. D. Noe, <a href="/A185399/b185399.txt">Table of n, a(n) for n = 1..100</a>
%H A185399 R. Mestrovic, <a href="http://arxiv.org/abs/1111.3057">Wolstenholme's theorem: Its Generalizations and Extensions in the last hundred and fifty years (1862-2011)</a>, arXiv:1111.3057 [math.NT], 2011.
%F A185399 a(n) = denominator(sum((k+1)/(p-k-1), k=0..p-2)), where p = the n-th prime. - _Gary Detlefs_, Jan 12 2012
%F A185399 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
%p A185399 f2:=proc(n) local p;
%p A185399 p:=ithprime(n);
%p A185399 denom(add(1/i,i=1..p-1));
%p A185399 end proc;
%p A185399 [seq(f2(n),n=1..20)];
%t A185399 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 *)
%o A185399 (PARI) a(n) = denominator(sum(k=1, prime(n)-1, 1/k)); \\ _Michel Marcus_, Dec 05 2018
%o A185399 (Magma) [Denominator(HarmonicNumber(NthPrime(n)-1)): n in [1..40]]; // _Vincenzo Librandi_, Dec 05 2018
%Y A185399 Cf. A001008, A002805 (numerators and denominators of harmonic numbers).
%Y A185399 Cf. A061002, A193758.
%K A185399 nonn
%O A185399 1,2
%A A185399 _N. J. A. Sloane_, Jan 21 2012