A139169 -id:A139169 - cp's OEIS frontend

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

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

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

cp's OEIS Frontend

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

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