A319852 -id:A319852 - cp's OEIS frontend

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

Alonso del Arte, Sep 29 2018

nonn

			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.

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.

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

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

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

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

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

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

Original entry on oeis.org

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

Alonso del Arte, Sep 30 2018

sign

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

Cf. A000079, A054850, A319852, A319857.

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

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

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

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) .

cp's OEIS Frontend

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

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