A122136 - OEIS

%I #4 Jan 02 2024 14:13:46

%S 2,13,19,29,104,29,111,79,778,47,73,163,1068,359,5233,885,142,20477,

%T 219,811,2524,13859,2203,56387,10966,75997,3331,6537,54968,1,23139,

%U 4457,87382,681,15449,239087,108,58061,159097,116041,1882,995,74901,7487

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

%C 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,...}.

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

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

%Y Cf. A122137, A122138, A122139.

%K frac,nonn

%O 1,1

%A _Alexander Adamchuk_, Aug 21 2006