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A135568 a(n) = floor( Product_{i=1..n} prime(i)/i ). 3
1, 2, 3, 5, 8, 19, 41, 101, 240, 614, 1782, 5024, 15492, 48859, 150069, 470216, 1557591, 5405758, 18319515, 64600395, 229331402, 797199637, 2862671427, 10330509932, 38308974332, 148638820408 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Does there exist an n such that (the product of the first n primes)/n! is an integer for n>3?

The answer to the question above is obviously no: for n>3 the denominator is a multiple of 4. - Emeric Deutsch, Mar 14 2008

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

FORMULA

a(n) = floor(product of the first n primes/n!).

a(n) = floor( A002110(n) / A000142(n) ).

EXAMPLE

a(5) = floor(2*3*5*7*11/5!) = floor(2310/120)=19.

MAPLE

a:=proc(n) options operator, arrow: floor(mul(ithprime(i)/i, i=1..n)) end proc: seq(a(n), n=1..25); # Emeric Deutsch, Mar 14 2008

MATHEMATICA

Table[Floor[Product[Prime[i]/i, {i, n}]], {n, 0, 25}] (* G. C. Greubel, Oct 19 2016 *)

CROSSREFS

Cf. A000040, A000142, A002110.

Sequence in context: A025071 A319644 A049908 * A103004 A102016 A002363

Adjacent sequences:  A135565 A135566 A135567 * A135569 A135570 A135571

KEYWORD

easy,nonn

AUTHOR

Ctibor O. Zizka, Feb 23 2008

EXTENSIONS

Corrected and extended by Emeric Deutsch, Mar 14 2008

STATUS

approved

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Last modified August 23 11:24 EDT 2019. Contains 326222 sequences. (Running on oeis4.)