A208768 The distinct values of A070198.

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

Author

Reinhard Zumkeller, Mar 01 2012

Keywords

• nonn

Comments

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

Links

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

Programs

Haskell

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

Python

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