A139184 -id:A139184 - cp's OEIS frontend

A139174 a(n) = (n!-4)/4.

5, 29, 179, 1259, 10079, 90719, 907199, 9979199, 119750399, 1556755199, 21794572799, 326918591999, 5230697471999, 88921857023999, 1600593426431999, 30411275102207999, 608225502044159999

Offset: 4

Artur Jasinski, Apr 11 2008

In the solution set of the equation, n! + s^2 = m^2, for any n>=4 the maximum value of s is (n!-4)/4. - Sudipta Mallick, Jul 27 2019

Sudipta Mallick, Table of n, a(n) for n = 4..400 (terms 4..300 from Vincenzo Librandi)

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

[(Factorial(n)-4)/4: n in [4..25]]; // Vincenzo Librandi, Jul 20 2011

Mathematica
```
Table[(n! - 4)/4, {n, 4, 20}]
```

a(n) = numerator(((n+2)!-4)/(7*(n+2)!)), with offset 2. [Gary Detlefs, Nov 07 2010]

E.g.f.: -exp(x)-(12+x^2*(-6+(-4+x)*x))/(12*(-1+x)). - Stefano Spezia, Sep 08 2019

Definition corrected by Gary Detlefs, Nov 07 2010

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

Original entry on oeis.org

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

A139175 a(n) = (n! - 5)/5.

Original entry on oeis.org

23, 143, 1007, 8063, 72575, 725759, 7983359, 95800319, 1245404159, 17435658239, 261534873599, 4184557977599, 71137485619199, 1280474741145599, 24329020081766399, 486580401635327999

Offset: 5

Artur Jasinski, Apr 11 2008

nonn

Original name: Natural numbers of the form (n!-5)/5.

Vincenzo Librandi, Table of n, a(n) for n = 5..300

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

[(Factorial(n)-5)/5: n in [5..25]]; // Vincenzo Librandi, Jul 20 2011

Mathematica
```
Table[(n! - 5)/5, {n, 5, 20}]
```

for(n=5,25, print1((n! -5)/5, ", ")) \\ G. C. Greubel, Oct 18 2018

E.g.f.: (120 - 60*x^2 - 40*x^3 - 15*x^4 + 19*x^5)/(120*(1-x)) - exp(x). - G. C. Greubel, Oct 18 2018

Corrected offset from 4 to 5 by Vincenzo Librandi, Jul 20 2011

New name from Jon E. Schoenfield, Oct 18 2018

A139176 a(n) = (n! - 6)/6.

Original entry on oeis.org

0, 3, 19, 119, 839, 6719, 60479, 604799, 6652799, 79833599, 1037836799, 14529715199, 217945727999, 3487131647999, 59281238015999, 1067062284287999, 20274183401471999, 405483668029439999

Offset: 3

Artur Jasinski, Apr 11 2008

nonn

Original name: Natural numbers of the form (n!-6)/6.

Vincenzo Librandi, Table of n, a(n) for n = 3..300

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

List([3..25],n->(Factorial(n)-6)/6); # Muniru A Asiru, Oct 20 2018

[(Factorial(n)-6)/6: n in [3..25]]; // Vincenzo Librandi, Jul 20 2011

seq((factorial(n)-6)/6,n=3..25); # Muniru A Asiru, Oct 20 2018

Mathematica
```
Table[(n! - 6)/6, {n, 3, 20}]
```

New name from Jon E. Schoenfield, Oct 19 2018

A139177 a(n) = (n! - 7)/7.

Original entry on oeis.org

719, 5759, 51839, 518399, 5702399, 68428799, 889574399, 12454041599, 186810623999, 2988969983999, 50812489727999, 914624815103999, 17377871486975999, 347557429739519999

Offset: 7

Artur Jasinski, Apr 11 2008

Original name: Natural numbers of the form (n!-7)/7.

Vincenzo Librandi, Table of n, a(n) for n = 7..300

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

List([7..25],n->(Factorial(n)-7)/7); # Muniru A Asiru, Oct 20 2018

[(Factorial(n)-7)/7: n in [7..25]]; // Vincenzo Librandi, Jul 20 2011

seq((factorial(n)-7)/7,n=7..25); # Muniru A Asiru, Oct 20 2018

Mathematica
```
Table[(n! - 7)/7, {n, 7, 20}]
```

New name from Jon E. Schoenfield, Oct 19 2018

A139183 a(n) = (n! - 8)/8.

Original entry on oeis.org

2, 14, 89, 629, 5039, 45359, 453599, 4989599, 59875199, 778377599, 10897286399, 163459295999, 2615348735999, 44460928511999, 800296713215999, 15205637551103999, 304112751022079999

Offset: 4

Artur Jasinski, Apr 11 2008

nonn

Original name: Natural numbers of the form (n!-8)/8.

Vincenzo Librandi, Table of n, a(n) for n = 4..300

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

List([4..25],n->(Factorial(n)-8)/8); # Muniru A Asiru, Oct 20 2018

[(Factorial(n)-8)/8: n in [4..25]]; // Vincenzo Librandi, Jul 20 2011

seq((factorial(n)-8)/8,n=4..25); # Muniru A Asiru, Oct 20 2018

Mathematica
```
Table[(n! - 8)/8, {n, 4, 20}]
```

New name from Jon E. Schoenfield, Oct 19 2018

A139173 a(n) = n!/3 - 1.

Original entry on oeis.org

1, 7, 39, 239, 1679, 13439, 120959, 1209599, 13305599, 159667199, 2075673599, 29059430399, 435891455999, 6974263295999, 118562476031999, 2134124568575999, 40548366802943999, 810967336058879999

Offset: 3

Artur Jasinski, Apr 11 2008

nonn

Original definition: Natural numbers of the form (n! - 3)/3.

Vincenzo Librandi, Table of n, a(n) for n = 3..300

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

Cf. A139191: primes in this sequence. - M. F. Hasler, Apr 09 2009

[Factorial(n)/3 -1: n in [3..25]]; // Vincenzo Librandi, Jul 20 2011

Mathematica
```
Table[(n! - 3)/3, {n, 3, 20}]
```

for(n=3,25, print1((n!-3)/3, ", ")) \\ G. C. Greubel, Oct 18 2018

E.g.f.: (6 - 3*x^2 - x^3)/(6*(1-x)) - exp(x). - G. C. Greubel, Oct 18 2018

Edited by M. F. Hasler, Apr 09 2009

A139185 a(n) = (n! - 10)/10.

Original entry on oeis.org

11, 71, 503, 4031, 36287, 362879, 3991679, 47900159, 622702079, 8717829119, 130767436799, 2092278988799, 35568742809599, 640237370572799, 12164510040883199, 243290200817663999

Offset: 5

Artur Jasinski, Apr 11 2008

Original name: Natural numbers of the form (n!-10)/10.

Vincenzo Librandi, Table of n, a(n) for n = 5..300

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

List([5..25],n->(Factorial(n)-10)/10); # Muniru A Asiru, Oct 20 2018

[(Factorial(n)-10)/10: n in [5..25]]; // Vincenzo Librandi, Jul 20 2011

seq((factorial(n)-10)/10,n=5..25); # Muniru A Asiru, Oct 20 2018

Mathematica
```
Table[(n! - 10)/10, {n, 5, 20}]
```

New name from Jon E. Schoenfield, Oct 19 2018

A290122 Primes of the form k!/9 - 1.

Original entry on oeis.org

79, 145297151999, 39520825343999, 711374856191999, 5676771352412159999, 1209874383379816906751999999, 982417999304411328282623999999, 29472539979132339848478719999999, 1529305899025149449590664397953433599999999

Offset: 1

Robert Price, Jul 19 2017

nonn

Robert Price, Table of n, a(n) for n = 1..12
Joe McLean, Interesting Sources of Probable Primes.
OpenPFGW Project, Primality Tester.

Cf. A139184, A139204, A290116, A290117, A290118, A290119, A290120, A290121, A290123.

Select[Table[k! / 9 - 1, {k, 6, 100}], PrimeQ[#]&]

a(n) = A139184(A139204(n)). - Elmo R. Oliveira, Apr 16 2025

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

cp's OEIS Frontend

A139174 a(n) = (n!-4)/4.

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

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A139175 a(n) = (n! - 5)/5.

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A139176 a(n) = (n! - 6)/6.

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Maple

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A139177 a(n) = (n! - 7)/7.

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GAP

Magma

Maple

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A139183 a(n) = (n! - 8)/8.

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Programs

GAP

Magma

Maple

Mathematica

Extensions

A139173 a(n) = n!/3 - 1.

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