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A319880 Difference between 2^n and the product of primes less than or equal to n. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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

LINKS

Table of n, a(n) for n=0..31.

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) .

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}]

PROG

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

CROSSREFS

Cf. A000079, A054850, A319852, A319857.

Sequence in context: A157341 A038036 A297793 * A133631 A137450 A321415

Adjacent sequences:  A319877 A319878 A319879 * A319881 A319882 A319883

KEYWORD

sign

AUTHOR

Alonso del Arte, Sep 30 2018

STATUS

approved

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Last modified January 21 04:02 EST 2021. Contains 340332 sequences. (Running on oeis4.)