A319880 Difference between 2^n and the product of primes less than or equal to n.

0, 1, 2, 2, 10, 2, 34, -82, 46, 302, 814, -262, 1786, -21838, -13646, 2738, 35506, -379438, -248366, -9175402, -8651114, -7602538, -5505386, -214704262, -206315654, -189538438, -155984006, -88875142, 45342586, -5932822318, -5395951406, -198413006482

Offset: 0

Author

Alonso del Arte, Sep 30 2018

Keywords

• sign

Comments

This sequence shows 2^n is neither a lower bound nor an upper bound for the primorials.

Crossrefs

Cf. A000079, A054850, A319852, A319857.

Programs

Maple

restart;
with(NumberTheory);
a := n -> 2^n-product(ithprime(i), i = 1 .. PrimeCounting(n)):
0, seq(a(n), n = 1 .. 15); # Stefano Spezia, Nov 05 2018

Mathematica

Table[2^n - Times@@Select[Range[n], PrimeQ], {n, 0, 31}]

PARI

a(n) = 2^n - prod(k=1, primepi(n), prime(k)); \\ Michel Marcus, Nov 05 2018

Formula

a(n) = 2^n - n#, where n# is the product of primes less than or equal to n (A034386).

a(n) = A000079(n) - A034386(n) .