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A319857 Difference between 4^n and the product of primes less than or equal to n. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 26 20:17 EDT 2021. Contains 346294 sequences. (Running on oeis4.)