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%I #20 May 06 2021 03:23:00
%S 2,6,14,30,75,62,126,254,510,1022,2046,4094,8190,16382,32766,65534
%N Integer k of the pairs (k, m) ordered by m with 1 < k < m such that k has the same prime divisors as m, and, k+1 has the same prime divisors as m+1.
%C First column of the array A343101.
%C Even integer 2^q - 2, q >= 2 is a term (A000918), and only 75 is known to be not of this form.
%H BxMO 2011, <a href="http://www.bxmo.org/problems/bxmo-problems-2011-fr.pdf">Third Benelux Mathematical Olympiad, Problème 1</a>.
%H <a href="/index/O#Olympiads">Index to sequences related to Olympiads</a>.
%e The corresponding pair to a(4) = 30 is (30, 960) because 30 = 2 * 3 * 5 and 960 = 2^5 * 3 * 5 while 961 = 31^2.
%e The corresponding pair to a(5) = 75 is (75, 1215) because 75 = 3 * 5^2 and 1215 = 5 * 3^5, while 76 = 2^2 * 19 and 1216 = 2^6 * 19.
%Y Cf. A000918, A087914 (2nd column), A343101 (array).
%K nonn,hard,more
%O 1,1
%A _Bernard Schott_, May 03 2021
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