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Search: id:A023195
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| A023195 |
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Prime numbers that are the sum of the divisors of some n. |
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+0
5
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| 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; listen)
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OFFSET
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1,1
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COMMENT
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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 (noe(AT)sspectra.com), 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 (mymontain(AT)yahoo.com), May 28 2005
Primes of the form 1 + p + p^2 + ... + p^k where p is prime.
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LINKS
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David W. Wilson, Table of n, a(n) for n=1..10000
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MATHEMATICA
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s[n_] := If[PrimeQ[n - 1], n - 1, (For[m = 1, m < n && DivisorSigma[ 1, m] != n, m++ ]; m)]; Do[If[s[Prime[n]] < Prime[n], Print[ Prime[n]]], {n, 92350}] (Firoozbakht)
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CROSSREFS
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Cf. A000668.
Sequence in context: A077314 A069246 A087578 this_sequence A100382 A152981 A112040
Adjacent sequences: A023192 A023193 A023194 this_sequence A023196 A023197 A023198
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KEYWORD
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nonn
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AUTHOR
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David W. Wilson (davidwwilson(AT)comcast.net)
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