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 A001275 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) 2
 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; text; internal format)
 OFFSET 1,1 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). 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). LINKS Amiram Eldar, Table of n, a(n) for n = 1..650 Karl K. Norton, Remarks on the number of factors of an odd perfect number, Acta Arith., 6 (1961), 365-374. FORMULA a(n) = prime(n)^2 + O(n^2/exp((log n)^(4/7 - e))) for any e > 0. a(n) = prime(A001276(n) + n - 1). - Amiram Eldar, Jul 12 2019 MATHEMATICA a[n_] := Module[{p = If[n == 1, 1, Prime[n - 1]], r = 1}, While[r <= 2, p = NextPrime[p]; r *= p/(p - 1)]; p]; Array[a, 50]  (* Amiram Eldar, Jul 12 2019 *) 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 CROSSREFS Cf. A001276. Sequence in context: A231722 A168612 A127178 * A058757 A278455 A060089 Adjacent sequences:  A001272 A001273 A001274 * A001276 A001277 A001278 KEYWORD nonn AUTHOR EXTENSIONS Comment, formula, program, and new definition from Charles R Greathouse IV, May 09 2011 STATUS approved

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Last modified February 18 02:57 EST 2020. Contains 332006 sequences. (Running on oeis4.)