A122136 Numerator of Sum[ Prime[k]^2, {k,1,n}] / Product[ Prime[k], {k,1,n}] = Numerator[ A024450[n] / A002110[n] ].

2, 13, 19, 29, 104, 29, 111, 79, 778, 47, 73, 163, 1068, 359, 5233, 885, 142, 20477, 219, 811, 2524, 13859, 2203, 56387, 10966, 75997, 3331, 6537, 54968, 1, 23139, 4457, 87382, 681, 15449, 239087, 108, 58061, 159097, 116041, 1882, 995, 74901, 7487

Offset: 1

Author

Alexander Adamchuk, Aug 21 2006

Keywords

• frac
• nonn

Comments

a(n) = 1 for n = {30,123,195,214,248,300,304,335,343,350,364,367,414,443,543,570,579,584,590,612,671,691,...} = A122137. a(n) is prime for n = {1,2,3,4,6,8,10,11,12,14,15,18,20,22,23,26,27,32,36,...} = A122138. Prime a(n) are listed in A122139 = {2,13,19,29,29,79,47,73,163,359,5233,20477,811,13859,2203,75997,3331,...}.

Crossrefs

Cf. A122137, A122138, A122139.

Programs

Mathematica

Table[Numerator[Sum[Prime[k]^2,{k,1,n}]/Product[Prime[k],{k,1,n}]],{n,1,100}]

Formula

a(n) = Numerator[ Sum[ Prime[k]^2, {k,1,n}] / Product[ Prime[k], {k,1,n}] ].