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A001275
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Smallest prime p such that the product of q/(q-1) over the primes from prime(n) to p is greater than 2.
(Formerly M4378 N1842)
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1
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3, 7, 23, 61, 127, 199, 337, 479, 677, 937, 1193, 1511, 1871, 2267, 2707, 3251, 3769, 4349, 5009, 5711, 6451, 7321, 8231, 9173, 10151, 11197, 12343, 13487, 14779, 16097, 17599, 19087, 20563, 22109, 23761, 25469, 27259, 29123, 31081, 33029
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| A perfect (or abundant) number with prime(n) as its lowest prime factor must be divisible by a prime greater than or equal to a(n).
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REFERENCES
| N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Karl K. Norton, Remarks on the number of factors of an odd perfect number, Acta Arith., 6 (1961), 365-374.
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FORMULA
| a(n) = prime(n)^2 + O(n^2/exp((log n)^(4/7 - e))) for any e > 0.
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PROG
| (PARI) a(n)=my(pr=1.); forprime(p=prime(n), default(primelimit), pr*=p/(p-1); if(pr>2, return(p))) \\ Charles R Greathouse IV, May 09, 2011
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CROSSREFS
| Cf. A001276.
Sequence in context: A179491 A168612 A127178 * A058757 A060089 A148689
Adjacent sequences: A001272 A001273 A001274 * A001276 A001277 A001278
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Comment, formula, program, and new definition from Charles R Greathouse IV, May 09, 2011
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