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%I #33 Feb 11 2024 09:22:00
%S 2,5,19,47,79,109,3667387
%N Primes that divide the numerator of the sum of the reciprocals of all smaller primes.
%C Exhaustive search finds no more terms among the first 10^7 primes.
%C Primes p that divide A024451(A000720(p)-1). - _Antti Karttunen_, Feb 08 2024
%F a(n) = A000040(1+A369972(n)). - _Antti Karttunen_, Feb 08 2024
%e Since 1/2 + 1/3 + 1/5 + 1/7 + 1/11 + 1/13 + 1/17 = 716167/510510 and 19 divides 716167, 19 is in the sequence.
%e Since there are no primes less than 2, the sum of their reciprocals is 0/1, and as 2 divides 0, it is therefore included as the first term of this sequence. - _Antti Karttunen_, Feb 08 2024
%o (PARI) lista(nn) = my(s = 0); forprime(p=2, nn, if (!(numerator(s) % p), print1(p, ", ")); s += 1/p; ); \\ _Michel Marcus_, Oct 09 2017, edited for the new, more inclusive definition by _Antti Karttunen_, Feb 08 2024
%Y Cf. A000040, A000720, A024451, A120289, A369972, A369973.
%K more,nonn
%O 1,1
%A _Logan J. Kleinwaks_, Oct 09 2017
%E Relaxed the definition to include 2 as the first term - _Antti Karttunen_, Feb 08 2024