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%I #23 Nov 13 2018 14:09:51
%S 0,3,14,58,250,994,4066,16174,65326,261934,1048366,4191994,16774906,
%T 67078834,268405426,1073711794,4294937266,17179358674,68718966226,
%U 274868207254,1099501928086,4398036811414,17592176344726,70368521084794,281474753617786,1125899683749754,4503599404277626
%N Difference between 4^n and the product of primes less than or equal to n.
%H Erdős Pál, <a href="http://combinatorica.hu/~p_erdos/1989-29.pdf">"Ramanujan and I"</a> Number Theory, Madras 1987. Springer, Berlin, Heidelberg, 1989. 1-17.
%H Leo Moser, <a href="https://cms.math.ca/10.4153/CMB-1959-017-9">"On the product of the primes not exceeding n"</a>, Canad. Math. Bull. 2 (1959), 119 - 121.
%F a(n) = 4^n - n#, where n# is the product of primes less than or equal to n (see A034386).
%e 4^5 = 1024. The primes less than or equal to 5 are 2, 3, and 5. Then 2 * 3 * 5 = 30 and hence a(5) = 1024 - 30 = 994.
%p restart;
%p with(NumberTheory);
%p a := n -> 4^n-product(ithprime(i), i = 1 .. PrimeCounting(n)):
%p 0, seq(a(n), n = 1 .. 15); # _Stefano Spezia_, Nov 06 2018
%t Table[4^n - Times@@Select[Range[n], PrimeQ], {n, 0, 31}]
%o (PARI) a034386(n) = my(v=primes(primepi(n))); prod(i=1, #v, v[i]) \\ after _Charles R Greathouse IV_ in A034386
%o a(n) = 4^n - a034386(n) \\ _Felix Fröhlich_, Nov 04 2018
%Y Cf. A000302 (4^n), A034386 (n#), A319852.
%K nonn
%O 0,2
%A _Alonso del Arte_, Sep 29 2018