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%I #10 Jun 01 2022 05:11:04
%S 1294298,9841094,158385500,1947793550,5833093013,11587121710,
%T 20944167840,22979821310,24604784814,267631935500,290672026412,
%U 956544588350,987988937343,2399283556900,2816075601855,4174608151758,4322550249043,6789218799999,10617595679778,16036630184409
%N Numbers k such that k, k+1 and k+2 are all divisible by the square of their largest prime factor.
%C Numbers k such that P(k)^2 | k, P(k+1)^2 | (k+1), and P(k+2)^2 | (k+2), where P(k) = A006530(k).
%C The data is from De Koninck and Moineau (2018).
%H Amiram Eldar, <a href="/A354560/b354560.txt">Table of n, a(n) for n = 1..60</a>
%H Jean-Marie De Koninck, <a href="https://bookstore.ams.org/mbk-64/297">Those Fascinating Numbers</a>, American Mathematical Society, 2009, p. 277, entry 1294298.
%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 1294298 = 2 * 61 * 103^2 is a term since P(1294298) = 103 and 103^2 | 1294298, 1294299 = 3^4 * 19 * 29^2, P(1294299) = 29 and 29^2 | 1294299, 1294300 = 2^2 * 5^2 * 7 * 43^2, P(1294300) = 43 and 43^2 | 1294300.
%Y Subsequence of A070003 and A354558.
%Y Cf. A006530, A071178.
%K nonn
%O 1,1
%A _Amiram Eldar_, May 30 2022