A139066 -id:A139066 - cp's OEIS frontend

A139161 a(n)=(prime(n)!+3)/3.

3, 41, 1681, 13305601, 2075673601, 118562476032001, 40548366802944001, 8617338912961658880001, 2947253997913233984847872000001, 2740946218059307605908520960000001

Offset: 2

Artur Jasinski, Apr 11 2008

nonn

Cf. A082672, A089085, A089130, A117141, A007749, A139056-A139066, A020458, A139068, A137390, A139070-A139075, A139148-A139157, A139159, A139160-A139166, A139089, A139168-A139170.

Mathematica
```
Table[(Prime[n]! + 3)/3, {n, 2, 30}]
```

A139072 Smallest parameter k such that (n+k!)/n is prime.

Original entry on oeis.org

1, 2, 3, 4, 7, 3, 11, 7, 8, 5, 13, 4, 28, 10, 7, 8, 43, 6, 21, 5, 7, 16, 48, 4, 14, 17, 9, 7, 241, 5, 61, 11, 17, 17, 8, 10, 44, 38, 16, 6, 131, 9, 63, 12, 6, 43, 73, 9, 15, 10, 19, 14, 64, 11, 12, 9, 24, 32, 641, 5, 89, 31, 8, 8, 14, 11, 71, 19, 25, 7, 151, 6, 78, 62, 15, 35, 15, 22, 87

Offset: 1

Artur Jasinski, Apr 07 2008

nonn

a(n) >= A002034(n). - Charles R Greathouse IV, Jul 15 2011

a(878) > 5000. - Jinyuan Wang, Apr 01 2020

Jinyuan Wang, Table of n, a(n) for n = 1..877

Cf. A082672, A089085, A089130, A117141, A007749, A139056-A139066, A020458, A139068, A137390, A139070-A139075, A136019, A136020, A136026, A136027.

a = {}; Do[k = 1; While[ ! PrimeQ[(k! + n)/n], k++ ]; AppendTo[a, k], {n, 1, 100}]; a

pr(n)=denominator(n)==1 && ispseudoprime(n)
a(n)=my(k);until(pr(k++!/n+1),);k \\ Charles R Greathouse IV, Jul 15 2011

A139074 a(n) = smallest prime p such that p!/n + 1 is prime, or 0 if no such prime exists.

Original entry on oeis.org

2, 2, 3, 5, 7, 3, 11, 7, 26737, 5, 13, 5

Offset: 1

Artur Jasinski, Apr 08 2008, Apr 21 2008

For the corresponding primes p see A139075.
a(9)>5000, a(13)>5000, a(22)>5000, a(23) = 1579. - Andrew V. Sutherland, Apr 21 2008, Apr 22 2008
a(10)=5,   a(11)=13, a(12)=5
a(14)=17,  a(15)=7,  a(16)=13,  a(17)=43, a(18)=7,
a(19)=31,  a(20)=5,  a(21)=7
a(24)=7,   a(25)=47, a(26)=17,  a(27)=17, a(28)=7,
a(29)=241, a(30)=5,  a(31)=61,  a(32)=11, a(33)=17,
a(34)=17,  a(35)=29, a(36)=11,  a(37)=61, a(38)=103,
a(39)=89,  a(40)=7,  a(41)=131, a(42)=11, a(43)=71,
a(44)=13,  a(45)=7,  a(46)=43,  a(47)=73, a(48)=67,
a(49)=347, a(50)=31, a(51)=19,  a(52)=17, a(53)=347,
a(54)=11,  a(55)=13, a(56)=13,  a(57)=31, a(58)=73,
a(59)=641, a(60)=5
a(23) = 1579. - Andrew V. Sutherland, Apr 11 2008.
Smallest daughter factorial prime p of order n, i.e. smallest prime of the form (p!+n)/n where p is prime.
For smallest mother factorial prime p of order n see A139075
For smallest father factorial prime p of order n see A139207
For smallest son factorial prime p of order n see A139206
Summary added by Robert Price, Nov 25 2010:
a(1:20)=2,2,3,5,7,3,11,7,26737,5,13,5,>60000,17,7,13,43,7,31,5
a(21:40)=7,>60000,1579,7,47,17,17,7,241,5,61,11,17,17,29,11,61,103,89,7
a(41:60)=131,11,71,13,7,43,73,67,347,31,19,17,347,11,13,13,31,73,641,5
a(61:80)=89,31,13,13,17,11,71,19,131,7,151,7,>10000,641,73,43,17,331,113,11
a(81:100)=13,67,>10000,7,1999,89,31,11,>10000,19,19,31,607,71,61,11,761,23,>10000,83

			a(1) = 2 because 2 is the first prime and 2!/1 + 1 = 3 is prime
a(2) = 2 because 2 is the first prime and 2!/2 + 1 = 2 is prime
a(3) = 3 because 3!/3 + 1 = 3 is prime

Cf. A082672, A089085, A089130, A117141, A007749, A139056-A139066, A020458, A139068, A137390, A139070-A139075, A136019, A136020, A136026, A136027.

a = {}; Do[k = 1; While[ ! PrimeQ[(Prime[k]! + n)/n], k++ ]; AppendTo[a, Prime[k]], {n, 1, 8}]; a

a(9)-a(12) by Robert Price, Dec 19 2010

A139156 a(n) = (n!+9)/9.

Original entry on oeis.org

81, 561, 4481, 40321, 403201, 4435201, 53222401, 691891201, 9686476801, 145297152001, 2324754432001, 39520825344001, 711374856192001, 13516122267648001, 270322445352960001, 5676771352412160001

Offset: 6

Artur Jasinski, Apr 11 2008

nonn

Amiram Eldar, Table of n, a(n) for n = 6..450

Cf. A007749, A020458, A082672, A089085, A089130, A117141, A139056-A139066, A139068, A137390, A139070-A139075, A139148-A139157, A139159, A139160, A139161, A139162.

Mathematica
```
Table[(n! + 9)/9, {n, 6, 30}]
```

Name corrected by Amiram Eldar, Oct 14 2024

A139092 a(n) = number of distinct prime divisors of (9+prime(n)!)/9.

Original entry on oeis.org

3, 3, 2, 2, 2, 3, 2, 3, 4, 4, 5, 3, 3, 6, 5, 2, 3, 4, 3, 3, 4, 4, 4, 3, 7, 3, 3

Offset: 4

Artur Jasinski, Apr 08 2008

Conjecture: all prime divisors in A139089 are distinct

a(31) >= 4. - Amiram Eldar, Feb 13 2020

FactorDB, Status of a(31) = (9+127!)/9.

Cf. A082672, A089085, A089130, A117141, A007749, A139056-A139066, A020458, A139068, A137390, A139070-A139075, A136019, A136020, A136026, A136027, A139089-A139092.

a = {}; Do[w = (Prime[n]! + 9)/9; AppendTo[a, w], {n, 4, 16}]; a
PrimeNu[(9+Prime[Range[4,25]]!)/9] (* Harvey P. Dale, Jul 25 2019 *)

a(n) = A001221(A139089(n)). - Amiram Eldar, Feb 13 2020

More terms from Jon E. Schoenfield, Jul 16 2010

a(23)-a(30) using factordb.com from Amiram Eldar, Feb 13 2020

A139149 a(n) = (n!+2)/2.

Original entry on oeis.org

2, 4, 13, 61, 361, 2521, 20161, 181441, 1814401, 19958401, 239500801, 3113510401, 43589145601, 653837184001, 10461394944001, 177843714048001, 3201186852864001, 60822550204416001, 1216451004088320001, 25545471085854720001, 562000363888803840001

Offset: 2

Artur Jasinski, Apr 11 2008

Also the number of (not necessarily maximal) cliques in the (n-1)-(weak) Bruhat graph. - Eric W. Weisstein, Jul 29 2018

			(1!+2)/2 = 3/2 is not an integer.
a(2) = (2!+2)/2 = 2.

Amiram Eldar, Table of n, a(n) for n = 2..450
Eric Weisstein's World of Mathematics, Bruhat Graph.
Eric Weisstein's World of Mathematics, Clique.

a(n) = (n!+m)/m: A038507 (m=1), this sequence (m=2), A139150 (m=3), A139151 (m=4), A139152 (m=5), A139153 (m=6), A139154 (m=7), A139155 (m=8), A139156 (m=9), A139157 (m=10).
Offsets for above sequences are Kempner numbers A002034.
For smallest number of the form (m!+n)/n see A139148.
Cf. A007749, A020458, A082672, A089085, A089130, A117141, A137390, A139056-A139066, A139068, A139070-A139075, A139157, A139159-A139162.

Mathematica
```
Table[(n! + 2)/2, {n, 2, 30}]
```

a(n)=n!/2+1 \\ Charles R Greathouse IV, Jun 20 2012

A139150 a(n) = (n!+3)/3.

Original entry on oeis.org

3, 9, 41, 241, 1681, 13441, 120961, 1209601, 13305601, 159667201, 2075673601, 29059430401, 435891456001, 6974263296001, 118562476032001, 2134124568576001, 40548366802944001, 810967336058880001

Offset: 3

Artur Jasinski, Apr 11 2008

nonn

			(2!+3)/3 = 5/3 is not an integer.
a(3) = (3!+3)/3 = 3.

Amiram Eldar, Table of n, a(n) for n = 3..450

Cf. A007749, A020458, A082672, A089085, A089130, A117141, A139056-A139066, A139068, A137390, A139070-A139075, A139148-A139157, A139159, A139160, A139161, A139162.

Mathematica
```
Table[(n! + 3)/3, {n, 3, 30}]
```

Name corrected by Amiram Eldar, Oct 13 2024

A139152 a(n) = (n!+5)/5.

Original entry on oeis.org

25, 145, 1009, 8065, 72577, 725761, 7983361, 95800321, 1245404161, 17435658241, 261534873601, 4184557977601, 71137485619201, 1280474741145601, 24329020081766401, 486580401635328001, 10218188434341888001

Offset: 5

Artur Jasinski, Apr 11 2008

nonn

Amiram Eldar, Table of n, a(n) for n = 5..450

Cf. A007749, A020458, A082672, A089085, A089130, A117141, A139056-A139066, A139068, A137390, A139070-A139075, A139148-A139157, A139159, A139160-A139162.

Mathematica
```
Table[(n! + 5)/5, {n, 5, 30}]
```

Name corrected by Amiram Eldar, Oct 14 2024

A139153 a(n) = (n!+6)/6.

Original entry on oeis.org

2, 5, 21, 121, 841, 6721, 60481, 604801, 6652801, 79833601, 1037836801, 14529715201, 217945728001, 3487131648001, 59281238016001, 1067062284288001, 20274183401472001, 405483668029440001, 8515157028618240001

Offset: 3

Artur Jasinski, Apr 11 2008

nonn

Amiram Eldar, Table of n, a(n) for n = 3..450

Cf. A007749, A020458, A082672, A089085, A089130, A117141, A139056-A139066, A139068, A137390, A139070-A139075, A139148-A139157, A139159, A139160, A139161, A139162.

Mathematica
```
Table[(n! + 6)/6, {n, 3, 30}]
```

Name corrected by Amiram Eldar, Oct 14 2024

A139154 a(n) = (n!+7)/7.

Original entry on oeis.org

721, 5761, 51841, 518401, 5702401, 68428801, 889574401, 12454041601, 186810624001, 2988969984001, 50812489728001, 914624815104001, 17377871486976001, 347557429739520001, 7298706024529920001

Offset: 7

Artur Jasinski, Apr 11 2008

nonn

Amiram Eldar, Table of n, a(n) for n = 7..450

Cf. A007749, A020458, A082672, A089085, A089130, A117141, A139056-A139066, A139068, A137390, A139070-A139075, A139148-A139157, A139159, A139160, A139161, A139162.

Mathematica
```
Table[(n! + 7)/7, {n, 7, 30}]
```

Name corrected by Amiram Eldar, Oct 14 2024

cp's OEIS Frontend

A139161 a(n)=(prime(n)!+3)/3.

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A139072 Smallest parameter k such that (n+k!)/n is prime.

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A139074 a(n) = smallest prime p such that p!/n + 1 is prime, or 0 if no such prime exists.

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A139156 a(n) = (n!+9)/9.

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A139092 a(n) = number of distinct prime divisors of (9+prime(n)!)/9.

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Formula

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A139149 a(n) = (n!+2)/2.

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PARI

A139150 a(n) = (n!+3)/3.

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A139152 a(n) = (n!+5)/5.

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A139153 a(n) = (n!+6)/6.

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