A139185 -id:A139185 - cp's OEIS frontend

A139172 a(n) = n!/2 - 1.

0, 2, 11, 59, 359, 2519, 20159, 181439, 1814399, 19958399, 239500799, 3113510399, 43589145599, 653837183999, 10461394943999, 177843714047999, 3201186852863999, 60822550204415999, 1216451004088319999, 25545471085854719999, 562000363888803839999, 12926008369442488319999

Offset: 2

Artur Jasinski, Apr 11 2008

Natural numbers of the form (n!-m)/m:
for m=1 n!-1 see A033312;
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

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

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

[(Factorial(n)-2)/2: n in [2..25]]; // Vincenzo Librandi, Jul 20 2011

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

a(n)=n!/2-1 \\ Charles R Greathouse IV, Apr 07 2012

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

A290123 Primes of the form k!/10 - 1.

Original entry on oeis.org

11, 71, 503, 3991679, 622702079, 35568742809599, 30488834461171386050150399999, 579712602074736798587973423157810910541235724473162595874586504971639017969389205625618453424974594047999999999999999999

Offset: 1

Robert Price, Jul 19 2017

nonn

Robert Price, Table of n, a(n) for n = 1..9
Joe McLean, Interesting Sources of Probable Primes.
OpenPFGW Project, Primality Tester.

Cf. A139185, A139205, A290116, A290117, A290118, A290119, A290120, A290121, A290122.

Select[Table[k! / 10 - 1, {k, 5, 100}], PrimeQ[#]&]

a(n) = A139185(A139205(n)). - Elmo R. Oliveira, Apr 16 2025

Missing terms inserted by Alois P. Heinz, Dec 05 2024

cp's OEIS Frontend

A139172 a(n) = n!/2 - 1.

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