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Numerator of determinant of n X n matrix with elements M[i,j] = (1+Prime[i])/Prime[i] if i=j and 1 otherwise.
2

%I #2 Mar 31 2012 13:20:27

%S 3,1,11,3,29,1,59,1,101,1,1,3,239,47,1,191,21,251,569,64,1,12,25,482,

%T 1061,1,1,98,1481,797,1721,926,3,8,3,1214,1,458,1,1544,99,1724,1213,

%U 1916,1,2,1,3,4889,853,5351,1,49,3041,2113,3301,6871,3571,2473,10,2661

%N Numerator of determinant of n X n matrix with elements M[i,j] = (1+Prime[i])/Prime[i] if i=j and 1 otherwise.

%C Many a(n), such as 3,11,29,59,101,239,569,1061,1481,1721,4889.., are primes of form p(1)+...+p(k)+1 where p(i) =i-th prime A053845. It appeares that all primes of this form are presented in a(n) in their natural order.

%C Indices n such that a(n) = 1 are {2,6,8,10,11,15,21,26,27,37,39,45,47,52,75,84,87,88,91,94,...} = A121744[n] Numbers n such that (1 + Sum[Prime[k],{k,1,n}]) = (1 + A007504[n]) divides primorial number p(n)# = Product[Prime[k],{k,1,n}] = A002110[n].

%F a(n) = numerator[Det[DiagonalMatrix[Table[1/Prime[i],{i,1,n}]]+1]].

%F a(n) = Numerator[ (1 + Sum[ Prime[k], {k,1,n} ]) / Product[ Prime[k], {k,1,n} ] ]. a(n) = Numerator[ (1 + A007504[n]) / A002110[n] ].

%t Numerator[Table[Det[DiagonalMatrix[Table[1/Prime[i],{i,1,n}]]+1],{n,1,70}]]

%t Table[Numerator[(1+Sum[Prime[k],{k,1,n}])/Product[Prime[k],{k,1,n}]],{n,1,100}]

%Y Cf. A024528, A053845.

%Y Cf. A121744, A007504, A002110.

%K frac,nonn

%O 1,1

%A _Alexander Adamchuk_, Jul 08 2006, Aug 19 2006