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%I #15 Nov 06 2018 03:00:55
%S 0,1,2,2,10,2,34,-82,46,302,814,-262,1786,-21838,-13646,2738,35506,
%T -379438,-248366,-9175402,-8651114,-7602538,-5505386,-214704262,
%U -206315654,-189538438,-155984006,-88875142,45342586,-5932822318,-5395951406,-198413006482
%N Difference between 2^n and the product of primes less than or equal to n.
%C This sequence shows 2^n is neither a lower bound nor an upper bound for the primorials.
%F a(n) = 2^n - n#, where n# is the product of primes less than or equal to n (A034386).
%F a(n) = A000079(n) - A034386(n) .
%p restart;
%p with(NumberTheory);
%p a := n -> 2^n-product(ithprime(i), i = 1 .. PrimeCounting(n)):
%p 0, seq(a(n), n = 1 .. 15); # _Stefano Spezia_, Nov 05 2018
%t Table[2^n - Times@@Select[Range[n], PrimeQ], {n, 0, 31}]
%o (PARI) a(n) = 2^n - prod(k=1, primepi(n), prime(k)); \\ _Michel Marcus_, Nov 05 2018
%Y Cf. A000079, A054850, A319852, A319857.
%K sign
%O 0,3
%A _Alonso del Arte_, Sep 30 2018