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 A023195 Prime numbers that are the sum of the divisors of some n. 26
 3, 7, 13, 31, 127, 307, 1093, 1723, 2801, 3541, 5113, 8011, 8191, 10303, 17293, 19531, 28057, 30103, 30941, 86143, 88741, 131071, 147073, 292561, 459007, 492103, 524287, 552793, 579883, 598303, 684757, 704761, 732541, 735307, 797161, 830833, 1191373 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS If n > 2 and sigma(n) is prime, then n must be an even power of a prime number. For example, 1093 = sigma(3^6). - T. D. Noe, Jan 20 2004 All primes of the form 2^n-1 (Mersenne primes) are in the sequence because if n is a natural number then sigma(2^(n-1)) = 2^n-1. So A000668 is a subsequence of this sequence. If sigma(n) is prime then n is of the form p^(q-1) where both p & q are prime (the proof is easy). - Farideh Firoozbakht, May 28 2005 Primes of the form 1 + p + p^2 + ... + p^k where p is prime. If n = sigma(p^k) is in the sequence, then k+1 is prime. - Franklin T. Adams-Watters, Dec 19 2011 Primes that are a repunit in a prime base. - Franklin T. Adams-Watters, Dec 19 2011. Except for 3, these primes are particular Brazilian primes belonging to A085104. These prime numbers are also Brazilian primes of the form (p^x - 1)/(p^y - 1), p prime, belonging to A003424, with here x is prime, and y = 1. [See section V.4 of Quadrature article in Links.] - Bernard Schott, Dec 25 2012 From Bernard Schott, Dec 25 2012: (Start) Others subsequences of this sequence: A053183 for 111_p = p^2 + p + 1 when p is prime. A190527 for 11111_p = p^4 + p^3 + p^2 + p + 1 when p is prime. A194257 for 1111111_p = p^6 + p^5 + p^4 + p^3 + p^2 + p + 1 when p is prime. (End) Subsequence of primes from A002191. - Michel Marcus, Jun 10 2014 LINKS David W. Wilson, Table of n, a(n) for n = 1..10000 Bernard Schott, Les nombres brésiliens, Quadrature, no. 76, avril-juin 2010, pages 30-38; included here with permission from the editors of Quadrature. EXAMPLE 307 = 1 + 17 + 17^2; 307 and 17 are primes. MATHEMATICA t={3}; lim=10^9; n=1; While[p=Prime[n]; k=2; s=1+p+p^2; s

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Last modified August 6 06:51 EDT 2024. Contains 374960 sequences. (Running on oeis4.)