

A282246


Primes p such that the sum of all primes <= p has no prime divisor > p.


1



2, 5, 11, 19, 23, 31, 41, 47, 59, 71, 83, 97, 101, 103, 109, 113, 127, 137, 157, 163, 167, 173, 179, 191, 197, 223, 227, 229, 233, 239, 241, 263, 269, 271, 317, 337, 349, 353, 367, 389, 401, 409, 433, 439, 449, 457, 461, 463, 467, 491, 521, 563, 571, 607, 613, 617, 631, 641, 653, 661, 701, 709, 719, 739, 757, 797
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OFFSET

1,1


COMMENTS

Number of terms < 10^k: 2, 12, 79, 523, 4124, 32678, 267850, etc. Compare these to A006880.  Robert G. Wilson v, Feb 09 2017
Primes p such that A006530(A007504(i)) <= p, where i is the index of p in A000040.  Felix FrÃ¶hlich, Feb 12 2017


LINKS

Robert G. Wilson v, Table of n, a(n) for n = 1..10000


EXAMPLE

5 is in the sequence for the sum of all primes <= 5 is 10, and 10 has no prime divisor > 5.
17 is not in the sequence for the corresponding sum is 58 which has a prime divisor > 17.


MATHEMATICA

p = s = 2; lst = {}; While[p < 1000, If[ FactorInteger[s][[1, 1]] <= p, AppendTo[lst, p]]; p = NextPrime@ p; s = s + p]; lst (* Robert G. Wilson v, Feb 09 2017 *)


PROG

(PARI) isok(n) = isprime(n) && (vecmax(factor(sum(k=1, primepi(n), prime(k)))[, 1]) <= n); \\ Michel Marcus, Feb 12 2017


CROSSREFS

Cf. A007504, A013916, A013917, A013918, A046731.
Sequence in context: A101057 A045362 A157978 * A045363 A336116 A031870
Adjacent sequences: A282243 A282244 A282245 * A282247 A282248 A282249


KEYWORD

nonn


AUTHOR

Emmanuel Vantieghem, Feb 09 2017


STATUS

approved



