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A001276
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Smallest k such that the product of q/(q-1) over the primes from prime(n) to prime(n+k-1) is greater than 2.
(Formerly M2650 N1057)
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1
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2, 3, 7, 15, 27, 41, 62, 85, 115, 150, 186, 229, 274, 323, 380, 443, 509, 577, 653, 733, 818, 912, 1010, 1114, 1222, 1331, 1448, 1572, 1704, 1845, 1994, 2138, 2289, 2445, 2609, 2774, 2948, 3127, 3311, 3502, 3699, 3900, 4112, 4324, 4546, 4775, 5016, 5255, 5493
(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 at least a(n) distinct primes.
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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) = li(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., k=0); forprime(p=prime(n), default(primelimit), pr*=p/(p-1); k++; if(pr>2, return(k))) \\ Charles R Greathouse IV, May 09, 2011
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CROSSREFS
| Cf. A001275.
Sequence in context: A098763 A066044 A066460 * A006884 A074742 A020873
Adjacent sequences: A001273 A001274 A001275 * A001277 A001278 A001279
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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 10, 2011
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