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 A001276 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) 2
 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; text; internal format)
 OFFSET 1,1 COMMENTS A perfect (or abundant) number with prime(n) as its lowest prime factor must be divisible by at least a(n) distinct primes. 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) = li(prime(n)^2) + O(n^2/exp((log n)^(4/7 - e))) for any e > 0. a(n) = pi(A001275(n)) - n + 1. - Amiram Eldar, Jul 12 2019 MATHEMATICA a[n_] := Module[{p = Prime[n], r = 1, k = 0}, While[r <= 2, r *= p/(p - 1); p = NextPrime[p]; k++]; k]; Array[a, 50] (* Amiram Eldar, Jul 12 2019 *) 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 CROSSREFS Cf. A001275. Sequence in context: A276047 A209658 A098763 * A006884 A074742 A020873 Adjacent sequences:  A001273 A001274 A001275 * A001277 A001278 A001279 KEYWORD nonn AUTHOR EXTENSIONS Comment, formula, program, and new definition from Charles R Greathouse IV, May 10 2011 STATUS approved

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Last modified April 1 10:33 EDT 2020. Contains 333159 sequences. (Running on oeis4.)