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A116536
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Numbers that can be expressed as the ratio between the product and the sum of consecutive prime numbers starting from 2.
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16
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1, 3, 125970, 1278362451795, 305565807424800745258151050335, 2099072522743338791053378243660769678400212601239922213271230, 330455532167461882998265688366895823334392289157931734871641555
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Let p(i) denote the i-th prime (A000040). Let F(m) = (Product_{i=1..m} p(i)) / (Sum_{i=1..m} p(i)). Sequence gives integer values of F(m) and A051838 gives corresponding values of m. - N. J. A. Sloane, Oct 01 2011
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REFERENCES
| G. Balzarotti and P. P. Lava, Le sequenze di numeri interi, Hoepli, 2008, p. 158.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..42
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FORMULA
| a(n) = A002110(A051838(n)) / A007504(A051838(n)). [Reinhard Zumkeller, Oct 03 2011]
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EXAMPLE
| a(1) = 1 because 2/2 = 1.
a(2) = 3 because (2*3*5)/(2+3+5) = 30/10 = 3.
a(3) = 125970 because (2*3*5*7*11*13*17*19)/(2+3+5+7+11+13+17+19) = 9699690/77 = 125790.
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MAPLE
| P:=proc(n) local i, j, pp, sp; pp:=1; sp:=0; for i from 1 by 1 to n do pp:=pp*ithprime(i); sp:=sp+ithprime(i); j:=pp/sp; if j=trunc(j) then print(j); fi; od; end: P(100);
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PROG
| (MAGMA) [p/s: n in [1..40] | IsDivisibleBy(p, s) where p is &*[NthPrime(i): i in [1..n]] where s is &+[NthPrime(i): i in [1..n]]]; // Bruno Berselli Bruno, Sep 30 2011
(Haskell)
import Data.Maybe (catMaybes)
a116536 n = a116536_list !! (n-1)
a116536_list = catMaybes $ zipWith div' a002110_list a007504_list where
div' x y | m == 0 = Just x'
| otherwise = Nothing where (x', m) = divMod x y
-- Reinhard Zumkeller, Oct 03 2011
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CROSSREFS
| Cf. A108552, A067111, A051838, A140763.
Cf. A141092.
Sequence in context: A171366 A086785 A159577 * A178505 A003544 A176586
Adjacent sequences: A116533 A116534 A116535 * A116537 A116538 A116539
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KEYWORD
| nonn,easy,changed
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AUTHOR
| Paolo P. Lava & Giorgio Balzarotti (paoloplava(AT)gmail.com), Mar 27 2006
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