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A319852 Difference between 3^n and the product of primes less than or equal to n.

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%I A319852 #20 Oct 22 2018 16:58:19
%S A319852 0,2,7,21,75,213,699,1977,6351,19473,58839,174837,529131,1564293,
%T A319852 4752939,14318877,43016691,128629653,386909979,1152561777,3477084711,
%U A319852 10450653513,31371359919,93920085957,282206443611,847065516573,2541642735459,7625374392117,22876569362091
%N A319852 Difference between 3^n and the product of primes less than or equal to n.
%C A319852 From Rosser (1941), it seems that the tightest possible upper bound is somewhere between e^n and 2.83^n. Therefore 3^n is the best possible upper bound with an integer base and integer exponent. - _Alonso del Arte_, Oct 22 2018
%H A319852 Barkley Rosser, <a href="https://www.jstor.org/stable/2371291">"Explicit Bounds for Some Functions of Prime Numbers"</a>, Amer. J. Math., 1941, 63 (1) p. 228, Lemma 21.
%H A319852 J. Barkley Rosser, Lowell Schoenfeld, <a href="http://projecteuclid.org/euclid.ijm/1255631807">Approximate formulas for some functions of prime numbers</a>, Illinois J. Math. 6 1962, 64-94.
%F A319852 a(n) = 3^n - n#, where n# = A034386(n) is the product of the primes less than or equal to n.
%e A319852 3^5 = 243. The primes less than or equal to 5 are: 2, 3, 5. Then 2 * 3 * 5 = 30 and hence a(5) = 243 - 30 = 213.
%t A319852 Table[3^n - Times@@Select[Range[n], PrimeQ], {n, 0, 26}]
%o A319852 (PARI) a(n) = 3^n-factorback(primes(primepi(n))) \\ _David A. Corneth_, Oct 22 2018
%Y A319852 Cf. A000244, A034386, A319857.
%K A319852 nonn
%O A319852 0,2
%A A319852 _Alonso del Arte_, Sep 29 2018
%E A319852 Many thanks to _Amiram Eldar_ for several bibliographic citations on this topic.