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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)
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

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), 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

N. J. A. Sloane

EXTENSIONS

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

STATUS

approved

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Last modified September 23 13:55 EDT 2017. Contains 292358 sequences.