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%I #12 Jun 04 2022 02:47:21
%S 242,2400,57121,499999,1012499,2825760,2829123,11859210,18279039,
%T 21093749,37218852,38740085,70799772,96393374,413428949,642837222,
%U 656356767,675975026,1065352364,1333564323,1418528255,2654744949,5547008142,8576868299,9515377949,10022519999
%N Numbers k such that P(k)^2 | k and P(k+1)^4 | (k+1), where P(k) = A006530(k) is the largest prime dividing k.
%H Daniel Suteu, <a href="/A354565/b354565.txt">Table of n, a(n) for n = 1..1908</a> (terms <= 10^17)
%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 242 = 2 * 11^2 is a term since P(242) = 11 and 11^2 | 242, 243 = 3^5, P(243) = 3, and 3^4 | 243.
%t p[n_] := FactorInteger[n][[-1, 2]]; Select[Range[10^6], p[#] > 1 && p[# + 1] > 3 &]
%o (Python)
%o from sympy import factorint
%o def c(n, e): f = factorint(n); return f[max(f)] >= e
%o def ok(n): return n > 1 and c(n, 2) and c(n+1, 4)
%o print([k for k in range(10**6) if ok(k)]) # _Michael S. Branicky_, May 30 2022
%Y Subsequence of A070003, A354558 and A354563.
%Y Cf. A006530, A071178, A354566.
%K nonn
%O 1,1
%A _Amiram Eldar_, May 30 2022