A139166 -id:A139166 - cp's OEIS frontend

A139159 a(n) = prime(n)! + 1.

3, 7, 121, 5041, 39916801, 6227020801, 355687428096001, 121645100408832001, 25852016738884976640001, 8841761993739701954543616000001, 8222838654177922817725562880000001, 13763753091226345046315979581580902400000001, 33452526613163807108170062053440751665152000000001

Offset: 1

Artur Jasinski, Apr 11 2008

Cf. A039716.
Cf. A093804, A103319.
Cf. A139160, A139161, A139162, A139163, A139164, A139165, A139166, A139089, A139168.

Prime[Range[12]]!+1 (* Vladimir Joseph Stephan Orlovsky, Apr 29 2008 *)

a(n)=prime(n)!+1 \\ Charles R Greathouse IV, Apr 29 2015

a(n) = A039716(n) + 1. - Michel Marcus, Nov 08 2013

More terms from Michel Marcus, Aug 10 2025

A139160 a(n)=(prime(n)!+2)/2.

Original entry on oeis.org

2, 4, 61, 2521, 19958401, 3113510401, 177843714048001, 60822550204416001, 12926008369442488320001, 4420880996869850977271808000001, 4111419327088961408862781440000001

Offset: 1

Artur Jasinski, Apr 11 2008

nonn

For numbers of the form (p(n)!+1)/1 see A139159
For numbers of the form (p(n)!+2)/2 see A139160
For numbers of the form (p(n)!+3)/3 see A139161
For numbers of the form (p(n)!+4)/4 see A139162
For numbers of the form (p(n)!+5)/5 see A139163
For numbers of the form (p(n)!+6)/6 see A139164
For numbers of the form (p(n)!+7)/7 see A139165
For numbers of the form (p(n)!+8)/8 see A139166
For numbers of the form (p(n)!+9)/9 see A139089
For numbers of the form (p(n)!+10)/10 see A139168
For offsets for above sequences see A139169
For smallest integers of the form (p(m)!+n)/n see A139170

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]! + 2)/2, {n, 1, 30}]
```

a(n)=prime(n)!/2 + 1 \\ Charles R Greathouse IV, Apr 29 2015

A139168 a(n) = (prime(n)! + 10)/10.

Original entry on oeis.org

13, 505, 3991681, 622702081, 35568742809601, 12164510040883201, 2585201673888497664001, 884176199373970195454361600001, 822283865417792281772556288000001

Offset: 3

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]! + 10)/10, {n, 3, 30}]
```

A139162 a(n)=(prime(n)!+4)/4.

Original entry on oeis.org

31, 1261, 9979201, 1556755201, 88921857024001, 30411275102208001, 6463004184721244160001, 2210440498434925488635904000001, 2055709663544480704431390720000001

Offset: 3

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]! + 4)/4, {n, 3, 30}]
```

A139170 a(n) = A136156(n) + 1.

Original entry on oeis.org

3, 2, 3, 31, 25, 2, 721, 16, 561, 13, 3628801, 11, 479001601, 361, 9, 316, 20922789888001, 281, 6402373705728001, 7, 241, 1814401, 1124000727777607680001, 6, 1596673, 239500801, 1478401, 181

Offset: 1

Artur Jasinski, Apr 11 2008

nonn

Cf. A136156.

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

a = {}; Do[m = 1; While[ ! IntegerQ[(n + Prime[m]!)/n], m++ ]; AppendTo[a, (n + Prime[m]!)/n], {n, 1, 100}]; a (*Artur Jasinski*)

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

Original entry on oeis.org

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}]
```

A139163 a(n) = (prime(n)!+5)/5.

Original entry on oeis.org

25, 1009, 7983361, 1245404161, 71137485619201, 24329020081766401, 5170403347776995328001, 1768352398747940390908723200001, 1644567730835584563545112576000001

Offset: 3

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.

A139163:=n->(ithprime(n)! + 5)/5; seq(A139163(n), n=3..15); # Wesley Ivan Hurt, Jan 23 2014

Mathematica
```
Table[(Prime[n]! + 5)/5, {n, 3, 30}]
```

a(n) = (prime(n)!+5)/5; \\ Michel Marcus, Jan 23 2014

A139169 a(n)=smallest k >= 1 such that n divides prime(k)!.

Original entry on oeis.org

1, 1, 2, 3, 3, 2, 4, 3, 4, 3, 5, 3, 6, 4, 3, 4, 7, 4, 8, 3, 4, 5, 9, 3, 5, 6, 5, 4, 10, 3, 11, 5, 5, 7, 4, 4, 12, 8, 6, 3, 13, 4, 14, 5, 4, 9, 15, 4, 7, 5, 7, 6, 16, 5, 5, 4, 8, 10, 17, 3, 18, 11, 4, 5, 6, 5, 19, 7, 9, 4, 20, 4, 21, 12, 5, 8, 5, 6, 22, 4, 5, 13, 23, 4, 7, 14, 10, 5, 24, 4, 6, 9, 11, 15

Offset: 1

Artur Jasinski, Apr 11 2008

nonn

Robert Israel, Table of n, a(n) for n = 1..10000

Indices of primes in A139171.

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

f:= proc(n) local F,m,Q,E,p;
  F:= ifactors(n)[2];
  m:= nops(F);
  Q:= map(t -> t[1],F);
  E:= map(t -> t[2],F);
  p:= max(Q)-1;
  do
    p:= nextprime(p);
    if andmap(i -> add(floor(p/Q[i]^j),j=1..floor(log[Q[i]](p))) >= E[i], [$1..m]) then return p fi;
  od
end proc:
f(1):= 2:
map(numtheory:-pi @ f, [$1..100]); # Robert Israel, Mar 07 2018

a = {}; Do[m = 1; While[ ! IntegerQ[Prime[m]!/n], m++ ]; AppendTo[a, m], {n, 1, 100}]; a

a(n) = forprime(p=2,, if (!(p! % n), return (primepi(p)))); \\ Michel Marcus, Mar 08 2018

A139171 a(n) = smallest prime number p such that p!/n is an integer.

Original entry on oeis.org

2, 2, 3, 5, 5, 3, 7, 5, 7, 5, 11, 5, 13, 7, 5, 7, 17, 7, 19, 5, 7, 11, 23, 5, 11, 13, 11, 7, 29, 5, 31, 11, 11, 17, 7, 7, 37, 19, 13, 5, 41, 7, 43, 11, 7, 23, 47, 7, 17, 11, 17, 13, 53, 11, 11, 7, 19, 29, 59, 5, 61, 31, 7, 11, 13, 11, 67, 17, 23, 7, 71, 7, 73, 37, 11, 19, 11, 13, 79, 7, 11

Offset: 1

Artur Jasinski, Apr 11 2008

Robert Israel, Table of n, a(n) for n = 1..10000
Wikipedia, Legendre's formula

Prime equivalent of Kempner numbers A002034.
For quotients p!/n see A139170.
For indices of primes in this sequence see A139169.
Cf. A082672, A089085, A089130, A117141, A007749, A139056-A139066, A139068, A137390, A139070-A139075, A139148-A139157, A139159, A139160-A139166, A139089, A139168-A139170.

f:= proc(n) local F,m,Q,E,p;
  F:= ifactors(n)[2];
  m:= nops(F);
  Q:= map(t -> t[1],F);
  E:= map(t -> t[2],F);
  p:= max(Q)-1;
  do
    p:= nextprime(p);
    if andmap(i -> add(floor(p/Q[i]^j),j=1..floor(log[Q[i]](p))) >= E[i], [$1..m]) then return p fi;
  od
end proc:
f(1):= 2:
map(f, [$1..100]); # Robert Israel, Mar 07 2018

a = {}; Do[m = 1; While[ ! IntegerQ[Prime[m]!/n], m++ ]; AppendTo[a, Prime[m]], {n, 1, 100}]; a

a(n) = forprime(p=2,, if (!(p! % n), return (p))); \\ Michel Marcus, Mar 08 2018

A139164 a(n) = (prime(n)!+6)/6.

Original entry on oeis.org

2, 21, 841, 6652801, 1037836801, 59281238016001, 20274183401472001, 4308669456480829440001, 1473626998956616992423936000001, 1370473109029653802954260480000001

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]! + 6)/6, {n, 2, 30}]
```

Offset corrected by Georg Fischer, Apr 04 2022

cp's OEIS Frontend

A139159 a(n) = prime(n)! + 1.

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A139160 a(n)=(prime(n)!+2)/2.

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A139168 a(n) = (prime(n)! + 10)/10.

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A139162 a(n)=(prime(n)!+4)/4.

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Mathematica

A139170 a(n) = A136156(n) + 1.

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

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Mathematica

A139163 a(n) = (prime(n)!+5)/5.

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Maple

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PARI

A139169 a(n)=smallest k >= 1 such that n divides prime(k)!.

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Maple

Mathematica

PARI

A139171 a(n) = smallest prime number p such that p!/n is an integer.

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Author

Keywords

Links

Crossrefs

Programs

Maple

Mathematica

PARI

A139164 a(n) = (prime(n)!+6)/6.

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