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A051452
a(n) = 1 + lcm(1..k) where k is the n-th prime power A000961(n).
3
2, 3, 7, 13, 61, 421, 841, 2521, 27721, 360361, 720721, 12252241, 232792561, 5354228881, 26771144401, 80313433201, 2329089562801, 72201776446801, 144403552893601, 5342931457063201, 219060189739591201
OFFSET
1,1
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)
PROG
(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
CROSSREFS
1 + A003418(A000961(n)), corresponds to distinct values of 1 + A003418.
Sequence in context: A089136 A092965 A051454 * A058017 A049536 A065508
KEYWORD
nonn
AUTHOR
STATUS
approved