Displaying 1-10 of 11 results found.
3, 7, 121, 5041, 39916801, 6227020801, 355687428096001, 121645100408832001, 25852016738884976640001, 8841761993739701954543616000001, 8222838654177922817725562880000001
CROSSREFS
Cf. A082672, A089085, A089130, A117141, A007749, A139056- A139066, A020458, A139068, A137390, A139070- A139075, A139148- A139157, A139159, A139160- A139166, A139089, A139168- A139170.
2, 4, 61, 2521, 19958401, 3113510401, 177843714048001, 60822550204416001, 12926008369442488320001, 4420880996869850977271808000001, 4111419327088961408862781440000001
COMMENTS
For numbers of the form (p(n)!+1)/1 see A139159For numbers of the form (p(n)!+2)/2 see A139160For numbers of the form (p(n)!+3)/3 see A139161For numbers of the form (p(n)!+4)/4 see A139162For numbers of the form (p(n)!+5)/5 see A139163For numbers of the form (p(n)!+6)/6 see A139164For numbers of the form (p(n)!+7)/7 see A139165For numbers of the form (p(n)!+8)/8 see A139166For numbers of the form (p(n)!+9)/9 see A139089For numbers of the form (p(n)!+10)/10 see A139168For offsets for above sequences see A139169For smallest integers of the form (p(m)!+n)/n see A139170
MATHEMATICA
Table[(Prime[n]! + 2)/2, {n, 1, 30}]
CROSSREFS
Cf. A082672, A089085, A089130, A117141, A007749, A139056- A139066, A020458, A139068, A137390, A139070- A139075, A139148- A139157, A139159, A139160- A139166, A139089, A139168- A139170.
16, 631, 4989601, 778377601, 44460928512001, 15205637551104001, 3231502092360622080001, 1105220249217462744317952000001, 1027854831772240352215695360000001
MATHEMATICA
Table[(Prime[n]! + 8)/8, {n, 3, 30}]
CROSSREFS
Cf. A082672, A089085, A089130, A117141, A007749, A139056- A139066, A020458, A139068, A137390, A139070- A139075, A139148- A139157, A139159, A139160- A139166, A139089, A139168- A139170.
a(n) = (prime(n)! + 10)/10.
+10
12
13, 505, 3991681, 622702081, 35568742809601, 12164510040883201, 2585201673888497664001, 884176199373970195454361600001, 822283865417792281772556288000001
MATHEMATICA
Table[(Prime[n]! + 10)/10, {n, 3, 30}]
CROSSREFS
Cf. A082672, A089085, A089130, A117141, A007749, A139056- A139066, A020458, A139068, A137390, A139070- A139075, A139148- A139157, A139159, A139160- A139166, A139089, A139168- A139170.
31, 1261, 9979201, 1556755201, 88921857024001, 30411275102208001, 6463004184721244160001, 2210440498434925488635904000001, 2055709663544480704431390720000001
MATHEMATICA
Table[(Prime[n]! + 4)/4, {n, 3, 30}]
CROSSREFS
Cf. A082672, A089085, A089130, A117141, A007749, A139056- A139066, A020458, A139068, A137390, A139070- A139075, A139148- A139157, A139159, A139160- A139166, A139089, A139168- A139170.
3, 41, 1681, 13305601, 2075673601, 118562476032001, 40548366802944001, 8617338912961658880001, 2947253997913233984847872000001, 2740946218059307605908520960000001
MATHEMATICA
Table[(Prime[n]! + 3)/3, {n, 2, 30}]
CROSSREFS
Cf. A082672, A089085, A089130, A117141, A007749, A139056- A139066, A020458, A139068, A137390, A139070- A139075, A139148- A139157, A139159, A139160- A139166, A139089, A139168- A139170.
a(n)=smallest k >= 1 such that n divides prime(k)!.
+10
3
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
MAPLE
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:
MATHEMATICA
a = {}; Do[m = 1; While[ ! IntegerQ[Prime[m]!/n], m++ ]; AppendTo[a, m], {n, 1, 100}]; a
PROG
(PARI) a(n) = forprime(p=2, , if (!(p! % n), return (primepi(p)))); \\ Michel Marcus, Mar 08 2018
CROSSREFS
Cf. A082672, A089085, A089130, A117141, A007749, A139056- A139066, A139068, A137390, A139070- A139075, A139148- A139157, A139159, A139160- A139166, A139089, A139168- A139170.
a(n) = smallest prime number p such that p!/n is an integer.
+10
3
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
MAPLE
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:
MATHEMATICA
a = {}; Do[m = 1; While[ ! IntegerQ[Prime[m]!/n], m++ ]; AppendTo[a, Prime[m]], {n, 1, 100}]; a
PROG
(PARI) a(n) = forprime(p=2, , if (!(p! % n), return (p))); \\ Michel Marcus, Mar 08 2018
CROSSREFS
Prime equivalent of Kempner numbers A002034. 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.
25, 1009, 7983361, 1245404161, 71137485619201, 24329020081766401, 5170403347776995328001, 1768352398747940390908723200001, 1644567730835584563545112576000001
MATHEMATICA
Table[(Prime[n]! + 5)/5, {n, 3, 30}]
CROSSREFS
Cf. A082672, A089085, A089130, A117141, A007749, A139056- A139066, A020458, A139068, A137390, A139070- A139075, A139148- A139157, A139159, A139160- A139166, A139089, A139168- A139170.
2, 21, 841, 6652801, 1037836801, 59281238016001, 20274183401472001, 4308669456480829440001, 1473626998956616992423936000001, 1370473109029653802954260480000001
MATHEMATICA
Table[(Prime[n]! + 6)/6, {n, 2, 30}]
CROSSREFS
Cf. A082672, A089085, A089130, A117141, A007749, A139056- A139066, A020458, A139068, A137390, A139070- A139075, A139148- A139157, A139159, A139160- A139166, A139089, A139168- A139170.
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