A319857 Difference between 4^n and the product of primes less than or equal to n.

0, 3, 14, 58, 250, 994, 4066, 16174, 65326, 261934, 1048366, 4191994, 16774906, 67078834, 268405426, 1073711794, 4294937266, 17179358674, 68718966226, 274868207254, 1099501928086, 4398036811414, 17592176344726, 70368521084794, 281474753617786, 1125899683749754, 4503599404277626

Offset

0,2

Links

Table of n, a(n) for n=0..26.

Erdős Pál, "Ramanujan and I" Number Theory, Madras 1987. Springer, Berlin, Heidelberg, 1989. 1-17.

Leo Moser, "On the product of the primes not exceeding n", Canad. Math. Bull. 2 (1959), 119 - 121.

Formula

a(n) = 4^n - n#, where n# is the product of primes less than or equal to n (see A034386).

Example

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.

Maple

restart;
with(NumberTheory);
a := n -> 4^n-product(ithprime(i), i = 1 .. PrimeCounting(n)):
0, seq(a(n), n = 1 .. 15); # Stefano Spezia, Nov 06 2018

Mathematica

Table[4^n - Times@@Select[Range[n], PrimeQ], {n, 0, 31}]

Prog

(PARI) a034386(n) = my(v=primes(primepi(n))); prod(i=1, #v, v[i]) \\ after Charles R Greathouse IV in A034386
a(n) = 4^n - a034386(n) \\ Felix Fröhlich, Nov 04 2018

Crossrefs

Cf. A000302 (4^n), A034386 (n#), A319852.

Sequence in context: A133444 A126875 A110526 * A038679 A151235 A151236

Adjacent sequences: A319854 A319855 A319856 * A319858 A319859 A319860

Keyword

nonn

Author

Alonso del Arte, Sep 29 2018

Status

approved