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%I #9 Sep 05 2020 08:18:12
%S 4,12,12,20,12,420,4,60,84,220,12,1092,4,60,924,340,12,103740,4,660,
%T 84,92,12,13260,44,60,1596,580,12,1861860,4,204,1932,20,132,3838380,4,
%U 60,84,153340,12,1361724,4,1380,77748,940,12,92820,4,660
%N a(n) = Max { k>0 : denominator(S(k,2n+1)) } where S(k,s)=sum(i=1,k,i^s*H(i,2)) - H(k,2)*H(k,-s) and H(k,r)=sum(i=1,k,1/i^r) are the generalized harmonic numbers.
%C The sequence D = (denominator(S(k, 2n+1)))_{k>0} is periodic for any n>0 . i.e. for n=2, D has period {1, 4, 12, 6, 6, 12, 12, 3, 1, 4, 4, 6, 6, 12, 12, 3, 3, 4, 4, 2, 6, 12, 12, 3, 3, 12, 4, 2, 2, 12, 12, 3, 3, 12, 12, 2, 2, 4, 12, 3, 3, 12, 12, 6, 2, 4, 4, 3, 3, 12, 12, 6, 6, 4, 4, 1, 3, 12, 12, 6, 6, 12, 4, 1, 1, 12, 12, 6, 6, 12, 12, 1} of length 72 and reaches 12 as maximum value, hence a(2)=12
%F a(n) = denominator(B(2*n)*(n+1/2)) where B() is Bernoulli number. - _Michael Somos_, Sep 05 2020
%o (PARI) H(n,r)=sum(i=1,n,1/i^r); S(n,s)=sum(k=1,n,k^s*H(k,2))-H(n,2)*H(n,-s); a(n)=vecmax(vector(100,i,denominator(S(i,2*n+1))))
%o (PARI) {a(n) = if(n<1, 0, denominator(bernfrac(2*n)*(n+1/2)))}; /* _Michael Somos_, Sep 05 2020 */
%K nonn
%O 1,1
%A _Benoit Cloitre_, Aug 10 2004
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