

A001276


Smallest k such that the product of q/(q1) over the primes from prime(n) to prime(n+k1) 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
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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

Table of n, a(n) for n=1..49.
Karl K. Norton, Remarks on the number of factors of an odd perfect number, Acta Arith., 6 (1961), 365374.


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/(p1); 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

N. J. A. Sloane


EXTENSIONS

Comment, formula, program, and new definition from Charles R Greathouse IV, May 10 2011


STATUS

approved



