A293457 Primes that divide the numerator of the sum of the reciprocals of all smaller primes.

2, 5, 19, 47, 79, 109, 3667387

Offset: 1

Author

Logan J. Kleinwaks, Oct 09 2017

Keywords

• more
• nonn

Comments

Exhaustive search finds no more terms among the first 10^7 primes.

Primes p that divide A024451(A000720(p)-1). - Antti Karttunen, Feb 08 2024

Examples

			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.
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
		

Crossrefs

Cf. A000040, A000720, A024451, A120289, A369972, A369973.

Programs

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

Formula

a(n) = A000040(1+A369972(n)). - Antti Karttunen, Feb 08 2024

Extensions

Relaxed the definition to include 2 as the first term - Antti Karttunen, Feb 08 2024