cp's OEIS Frontend

A354565 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.

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