A051452 a(n) = 1 + lcm(1..k) where k is the n-th prime power A000961(n).

2, 3, 7, 13, 61, 421, 841, 2521, 27721, 360361, 720721, 12252241, 232792561, 5354228881, 26771144401, 80313433201, 2329089562801, 72201776446801, 144403552893601, 5342931457063201, 219060189739591201

Offset: 1

Author

Labos Elemer

Keywords

• nonn

Comments

From Daniel Forgues, Apr 27 2014: (Start)

Factorizations:

2, 3, 7, 13, 61, 421 are primes;

841 = 29^2;

2521 is prime;

27721 = 19*1459, 360361 = 89*4049, 720721 = 71*10151,

12252241 = 1693*7237;

232792561 is prime;

5354228881 = 6659*804059;

26771144401 is prime;

80313433201 = 331*11239*21589, 2329089562801 = 101*271*2311*36821;

72201776446801 is prime.

Very likely contains an infinite number of primes (see A049536). (End)

Crossrefs

1 + A003418(A000961(n)), corresponds to distinct values of 1 + A003418.

Cf. A049536, A049537, A051454, A208768.

Programs

PARI

print1(2);t=1;for(n=2,100,if(t%n, t=lcm(t,n); print1(", "t+1))) \\ Charles R Greathouse IV, Jan 04 2013

Python

from math import prod
from sympy import primepi, integer_nthroot, integer_log, primerange
def A051452(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 1+prod(p**integer_log(m, p)[0] for p in primerange(m+1)) # Chai Wah Wu, Aug 15 2024