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A186720 As p runs through the primes, sequence gives denominator of Sum_{k=1..p-1} 1/k^2. 2

%I #16 Nov 25 2017 16:31:27

%S 1,4,144,3600,1270080,153679680,519437318400,150117385017600,

%T 221193371393280,6450247552370862240000,5424658191543895143840000,

%U 20852386088294732932920960000,28546916554875489385168794240000,6855338104106528236638391873920000,12675520154492970709544386574878080000

%N As p runs through the primes, sequence gives denominator of Sum_{k=1..p-1} 1/k^2.

%H 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.

%p f2:=proc(n) local p;

%p p:=ithprime(n);

%p denom(add(1/i^2,i=1..p-1));

%p end proc;

%p [seq(f2(n),n=1..20)];

%t a[n_] := HarmonicNumber[Prime[n] - 1, 2] // Denominator;

%t Array[a, 15] (* _Jean-François Alcover_, Nov 25 2017 *)

%Y Cf. A125551, A061002.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Jan 21 2012

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Last modified April 19 03:16 EDT 2024. Contains 371782 sequences. (Running on oeis4.)