This site is supported by donations to The OEIS Foundation.

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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) 1
 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 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. 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 18 04:47 EST 2019. Contains 319269 sequences. (Running on oeis4.)