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A208768 The distinct values of A070198.

%I A208768 #32 Aug 15 2024 02:02:17
%S A208768 0,1,5,11,59,419,839,2519,27719,360359,720719,12252239,232792559,
%T A208768 5354228879,26771144399,80313433199,2329089562799,72201776446799,
%U A208768 144403552893599,5342931457063199,219060189739591199,9419588158802421599,442720643463713815199
%N A208768 The distinct values of A070198.
%C A208768 The terms of A070198, and duplicates removed.
%C A208768 a(n) = A051451(n) - 1 = A051452(n) - 2.
%C A208768 From _Daniel Forgues_, Apr 27 2014: (Start)
%C A208768 Factorizations:
%C A208768   5, 11, 59, 419, 839 are primes;
%C A208768   2519 = 11*229, 27719 = 53*523, 360359 = 173*2083,
%C A208768   720719 = 31*67*347, 12252239 = 29*647*653;
%C A208768   232792559, 5354228879 are primes;
%C A208768   26771144399 = 47*12907*44131, 80313433199 = 29*61*45400471;
%C A208768   2329089562799 is prime;
%C A208768   72201776446799 = 37*149*239*1091*50227;
%C A208768   144403552893599 is prime;
%C A208768 Very likely contains an infinite number of primes (see A057824). (End)
%C A208768 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
%H A208768 Reinhard Zumkeller, <a href="/A208768/b208768.txt">Table of n, a(n) for n = 1..250</a>
%o A208768 (Haskell)
%o A208768 import Data.List (nub)
%o A208768 a208768 n = a208768_list !! (n-1)
%o A208768 a208768_list = nub a070198_list
%o A208768 (Python)
%o A208768 from math import prod
%o A208768 from sympy import primepi, integer_nthroot, integer_log, primerange
%o A208768 def A208768(n):
%o A208768     def f(x): return int(n+x-1-sum(primepi(integer_nthroot(x,k)[0]) for k in range(1,x.bit_length())))
%o A208768     m, k = n, f(n)
%o A208768     while m != k:
%o A208768         m, k = k, f(k)
%o A208768     return prod(p**integer_log(m, p)[0] for p in primerange(m+1))-1 # _Chai Wah Wu_, Aug 15 2024
%K A208768 nonn
%O A208768 1,3
%A A208768 _Reinhard Zumkeller_, Mar 01 2012