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

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

Offset

1,1

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

Links

Table of n, a(n) for n=1..7.

Formula

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

Example

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

Prog

(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

Crossrefs

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

Sequence in context: A140761 A077323 A215274 * A304782 A184435 A112266

Adjacent sequences: A293454 A293455 A293456 * A293458 A293459 A293460

Keyword

more,nonn

Author

Logan J. Kleinwaks, Oct 09 2017

Extensions

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

Status

approved