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A293457 Primes that divide the numerator of the sum of the reciprocals of all smaller primes. 3
2, 5, 19, 47, 79, 109, 3667387 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A140761 A077323 A215274 * A304782 A184435 A112266
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

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Last modified April 22 09:25 EDT 2024. Contains 371894 sequences. (Running on oeis4.)