A139172 Natural numbers of the form (n!-2)/2.

0, 2, 11, 59, 359, 2519, 20159, 181439, 1814399, 19958399, 239500799, 3113510399, 43589145599, 653837183999, 10461394943999, 177843714047999, 3201186852863999, 60822550204415999, 1216451004088319999

Offset

2,2

Comments

Natural numbers of the form (n!-m)/m:

for m=1 n!-1 see A033312;

for m=2 (n!-2)/2 see A139172;

for m=3 (n!-3)/3 see A139173;

for m=4 (n!-4)/4 see A139174;

for m=5 (n!-5)/5 see A139175;

for m=6 (n!-6)/6 see A139176;

for m=7 (n!-7)/7 see A139177;

for m=8 (n!-8)/8 see A139183;

for m=9 (n!-9)/9 see A139184;

for m=10 (n!-10)/10 see A139185.

From Artur Jasinski, Oct 14 2008: (Start)

a(n) = Number of numbers removed in first step of Eratosthenes's sieve for n!

a(5)=A145532(1), a(6)=A145533(1), a(7)=A145534(1), a(8)=A145535(1), a(9)=A145536(1), a(10)=A145537(1). (End)

Generally, for n >= m, the formula a(n) = n*(a(n-1) + 1) - 1 applies to all natural numbers of the form (n!-m)/m, m >= 2. - Bob Selcoe, Mar 28 2015

Links

Vincenzo Librandi, Table of n, a(n) for n = 2..300

Formula

a(n) = Sum_{k=1..floor(n/2)} s(n,n-2*k), where s(n,k) are Stirling numbers of the first kind, A048994. - Mircea Merca, Apr 07 2012

a(n) = n*(a(n-1) + 1) - 1. - Bob Selcoe, Mar 28 2015

Mathematica

Table[(n! - 2)/2, {n, 2, 20}]

Prog

(Magma) [(Factorial(n)-2)/2: n in [2..25]]; // Vincenzo Librandi, Jul 20 2011
(PARI) a(n)=n!/2-1 \\ Charles R Greathouse IV, Apr 07 2012

Crossrefs

Cf. A033312, A139172, A139173, A139174, A139175, A139176, A139177, A139183, A139184.

Sequence in context: A210646 A054564 A280674 * A228868 A290116 A251180

Adjacent sequences: A139169 A139170 A139171 * A139173 A139174 A139175

Keyword

nonn,easy

Author

Artur Jasinski, Apr 11 2008

Status

approved