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A051283 Numbers k such that if one writes k = Product p_i^e_i (p_i primes) and P = max p_i^e_i, then k/P > P.

%I A051283 #38 Jul 02 2025 16:01:58
%S A051283 30,60,70,84,90,105,120,126,132,140,154,165,168,180,182,195,198,210,
%T A051283 220,231,234,252,260,264,273,280,286,306,308,312,315,330,336,340,357,
%U A051283 360,364,374,380,385,390,396,399,408,418,420,429,440,442,455,456,462
%N A051283 Numbers k such that if one writes k = Product p_i^e_i (p_i primes) and P = max p_i^e_i, then k/P > P.
%C A051283 Numbers k such that A346418(k) > 1 (conjectured). - _Amiram Eldar_, Jul 16 2021
%C A051283 Numbers k for which A354933(k) > A034699(k), i.e., where A354995(k) > 0 (conjectured).-  _Antti Karttunen_, Jun 19 2022
%H A051283 Reinhard Zumkeller, <a href="/A051283/b051283.txt">Table of n, a(n) for n = 1..10000</a>
%F A051283 a(n) = A080170(n) + 1 (conjectured). - _Ralf Stephan_, Feb 20 2004
%e A051283 120 = 2^3*3^1*5^1, P = 2^3 = 8. 120 is included because 120/8 = 15 > 8.
%t A051283 ok[n_] := n > Max[Power @@@ FactorInteger[n]]^2; Select[Range[465], ok] (* _Jean-François Alcover_, Apr 11 2011 *)
%o A051283 (Haskell)
%o A051283 a051283 n = a051283_list !! (n-1)
%o A051283 a051283_list = filter (\x -> (a034699 x) ^ 2 < x) [1..]
%o A051283 -- _Reinhard Zumkeller_, May 30 2013
%o A051283 (PARI) lista(nn) = for(k=2, nn, f=factor(k); if(k>vecmax(vector(#f[, 1], i, f[i, 1]^f[i, 2]))^2, print1(k, ", "))); \\ _Jinyuan Wang_, Feb 28 2020
%Y A051283 Cf. A034699, A080170, A110612, A346418, A354933, A354995, A354996 (characteristic function).
%K A051283 nonn,easy,nice
%O A051283 1,1
%A A051283 _Leroy Quet_
%E A051283 More terms from _James Sellers_, Dec 11 1999