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A354562 Numbers k such that k and k+1 are both divisible by the cube of their largest prime factor.

%I A354562 #23 May 31 2022 02:17:24
%S A354562 6859,11859210,18253460,38331320423,41807225999,49335445119,
%T A354562 50788425848,67479324240,203534609200,245934780371,250355343420,
%U A354562 581146348824,779369813871,1378677994836,2152196307260,2730426690524,3616995855087,5473549133744,6213312123347,6371699408179,8817143116903
%N A354562 Numbers k such that k and k+1 are both divisible by the cube of their largest prime factor.
%C A354562 Numbers k such that P(k)^3 | k and P(k+1)^3 | (k+1), where P(k) = A006530(k).
%C A354562 a(1)-a(5) and a(7) are from De Koninck (2009).
%H A354562 David A. Corneth, <a href="/A354562/b354562.txt">Table of n, a(n) for n = 1..81</a> (terms <= 10^15)
%H A354562 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 A354562 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 A354562 6859 = 19^3 is a term since P(6859) = 19 and 19^3 | 6859, 6860 = 2^2 * 5 * 7^3, P(6860) = 7 and 7^3 | 6860.
%t A354562 q[n_] := FactorInteger[n][[-1, 2]] > 2; Select[Range[2*10^7], q[#] && q[# + 1] &]
%o A354562 (Python)
%o A354562 from sympy import factorint
%o A354562 def c(n): f = factorint(n); return f[max(f)] >= 3
%o A354562 def ok(n): return n > 1 and c(n) and c(n+1)
%o A354562 print([k for k in range(10**5) if ok(k)]) # _Michael S. Branicky_, May 30 2022
%Y A354562 Subsequence of A070003, A354558 and A354561.
%Y A354562 Intersection of A354563 and A354564.
%Y A354562 Cf. A006530, A071178.
%K A354562 nonn
%O A354562 1,1
%A A354562 _Amiram Eldar_, May 30 2022
%E A354562 a(6) and more terms from _David A. Corneth_, May 30 2022