%I #8 May 30 2022 16:31:54
%S 1,8,6859,11859210
%N a(n) is the least number k such that P(k)^n | k and P(k+1)^n | (k+1), where P(k) = A006530(k) is the largest prime dividing k, or -1 if no such k exists.
%C a(1) = 1 since P(1) = 1 by convention. Without this convention we would have a(1) = 2.
%C a(5) <= 437489361912143559513287483711091603378 (De Koninck, 2009).
%H Jean-Marie De Koninck, <a href="https://bookstore.ams.org/mbk-64/193">Those Fascinating Numbers</a>, American Mathematical Society, 2009, p. 173, entry 6859.
%H Jean-Marie De Koninck and Matthieu Moineau, <a href="http://emis.muni.cz/journals/JIS/VOL21/DeKoninck/dek22.html">Consecutive Integers Divisible by a Power of their Largest Prime Factor</a>, J. Integer Seq., Vol. 21 (2018), Article 18.9.3.
%e a(2) = 8 since 8 = 2^3, P(8) = 2 and 2^2|8, 9 = 3^2, P(9) = 3 and 3^2 | 9, and 8 is the least number with this property.
%e a(3) = 6859 since 6859 = 19^3, P(6859) = 19 and 19^3 | 6859, 6860 = 2^2 * 5 * 7^3, P(6860) = 7 and 7^3 | 6860, and 6859 is the least number with this property.
%Y Cf. A006530, A071178, A354558, A354562.
%K nonn,more,bref
%O 1,2
%A _Amiram Eldar_, May 30 2022