A057824 -id:A057824 - cp's OEIS frontend

A049536 Primes of the form lcm(1, ..., n) + 1 = A003418(n) + 1.

2, 3, 7, 13, 61, 421, 2521, 232792561, 26771144401, 72201776446801, 442720643463713815201, 718766754945489455304472257065075294401, 6676878045498705789701874602220118271269436344024536001

Offset: 1

Labos Elemer

nonn

			Lcm(9) + 1 = lcm(10) + 1 = 2521, a prime.

Harvey P. Dale, Table of n, a(n) for n = 1..16

Subsequence of A070858.

Cf. A003418, A049537, A057824.

Select[Table[LCM@@Range[n]+1,{n,150}],PrimeQ]//Union (* Harvey P. Dale, May 31 2017 *)

N=1; print1(2); for(n=1,1e3, if(isprimepower(n,&p), N*=p; if(isprime(N+1), print1(", "N+1)))) \\ Charles R Greathouse IV, Nov 18 2015

A208768 The distinct values of A070198.

Original entry on oeis.org

0, 1, 5, 11, 59, 419, 839, 2519, 27719, 360359, 720719, 12252239, 232792559, 5354228879, 26771144399, 80313433199, 2329089562799, 72201776446799, 144403552893599, 5342931457063199, 219060189739591199, 9419588158802421599, 442720643463713815199

Offset: 1

Reinhard Zumkeller, Mar 01 2012

nonn

The terms of A070198, and duplicates removed.
a(n) = A051451(n) - 1 = A051452(n) - 2.
From Daniel Forgues, Apr 27 2014: (Start)
Factorizations:
  5, 11, 59, 419, 839 are primes;
  2519 = 11*229, 27719 = 53*523, 360359 = 173*2083,
  720719 = 31*67*347, 12252239 = 29*647*653;
  232792559, 5354228879 are primes;
  26771144399 = 47*12907*44131, 80313433199 = 29*61*45400471;
  2329089562799 is prime;
  72201776446799 = 37*149*239*1091*50227;
  144403552893599 is prime;
Very likely contains an infinite number of primes (see A057824). (End)
A more natural (compare with A051452) name for the sequence: lcm(1, ..., k) - 1, where k is the n-th prime power A000961(n). - Daniel Forgues, May 09 2014

Reinhard Zumkeller, Table of n, a(n) for n = 1..250

import Data.List (nub)
a208768 n = a208768_list !! (n-1)
a208768_list = nub a070198_list

from math import prod
from sympy import primepi, integer_nthroot, integer_log, primerange
def A208768(n):
    def f(x): return int(n+x-1-sum(primepi(integer_nthroot(x,k)[0]) for k in range(1,x.bit_length())))
    m, k = n, f(n)
    while m != k:
        m, k = k, f(k)
    return prod(p**integer_log(m, p)[0] for p in primerange(m+1))-1 # Chai Wah Wu, Aug 15 2024

A385564 Prime powers k such that lcm(1, 2, 3, ..., k)-1 is prime.

Original entry on oeis.org

3, 4, 5, 7, 8, 19, 23, 29, 32, 47, 61, 97, 181, 233, 307, 401, 887, 1021, 1087, 1361, 1481, 2053, 2293, 5407, 5857, 11059, 14281, 27277, 27803, 36497, 44987, 53017

Offset: 1

Jeppe Stig Nielsen, Jul 03 2025

nonn

The prime associated with each a(n) is A057824(n).

a(33) > 10^5. Up to 10^5, contains 4, 8, 32 not in subsequence A154524. - Michael S. Branicky, Jul 04 2025

			k=32 is a prime power, so point at which A003418 attains a new value, namely lcm(1, 2, 3, ..., 32) = 144403552893600, and by subtracting one we get 144403552893599 which is a prime number, so 32 is a member of the sequence.

Intersection of A057825 and A000961.
Supersequence of A154524.
Cf. A057824, A051453, A003418.

Select[Range[6000],PrimePowerQ[#]&&PrimeQ[Fold[LCM,Range[#]]-1]&] (* James C. McMahon, Jul 09 2025 *)

L=1;for(k=2,6000,!isprimepower(k,&p)&&next();L*=p;ispseudoprime(L-1)&&print1(k,", "))

a(31)-a(32) from Michael S. Branicky, Jul 03 2025

A057822 Smaller of pair of twin primes whose average is lcm(1,...,m) for some m.

Original entry on oeis.org

5, 11, 59, 419, 232792559, 442720643463713815199

Offset: 1

Labos Elemer, Nov 08 2000

Known values of m such that lcm(1,...,m) is a twin prime mean value are as follows: {3, 4, 5, 6, 7, 19, 20, 21, 22, 47, 48}.
No more such primes occurs below m < 2000.
No more such primes occurs below m < 30000. - Amiram Eldar, Aug 18 2024

			419 and 421 are twin primes, (419 + 421)/2 = 420 = lcm(1,2,3,4,5,6,7).

Intersection of A057824 and {A049536(n)-2}.

Cf. A003418, A051451, A057706.

Select[FoldList[LCM, Select[Range[50], PrimePowerQ]] - 1, And @@ PrimeQ[# + {0, 2}] &] (* Amiram Eldar, Aug 18 2024 *)

lista(nn=50) = {for (i=1, nn, if (isprimepower(i), if (isprime(p=lcm([2..i])-1) && isprime(p+2), print1(p, ", "));););} \\ Michel Marcus, Aug 25 2019

cp's OEIS Frontend

A049536 Primes of the form lcm(1, ..., n) + 1 = A003418(n) + 1.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI

A208768 The distinct values of A070198.

Views

Author

Keywords

Comments

Links

Programs

Haskell

Python

A385564 Prime powers k such that lcm(1, 2, 3, ..., k)-1 is prime.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

PARI

Extensions

A057822 Smaller of pair of twin primes whose average is lcm(1,...,m) for some m.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

PARI