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A122146 Numbers k such that q(k) = M(k) and 4*q(k) <= k, where q(k) is the largest prime divisor of k and M(k) is the largest prime power divisor of k.

%I A122146 #14 May 23 2024 04:27:49
%S A122146 20,28,30,35,42,44,52,55,60,65,66,68,70,76,77,78,84,85,88,91,92,95,99,
%T A122146 102,104,105,110,114,115,116,117,119,124,130,132,133,136,138,140,143,
%U A122146 145,148,152,153,154,155,156,161,164,165,170,171,172,174,182,184,185
%N A122146 Numbers k such that q(k) = M(k) and 4*q(k) <= k, where q(k) is the largest prime divisor of k and M(k) is the largest prime power divisor of k.
%H A122146 Amiram Eldar, <a href="/A122146/b122146.txt">Table of n, a(n) for n = 1..10000</a>
%t A122146 Select[Range[200], Max[Power @@@ (f = FactorInteger[#])] == f[[-1, 1]] <= #/4 &] (* _Amiram Eldar_, May 23 2024 *)
%o A122146 (PARI) isok(k) = {my(f = factor(k), pm = 0); if(k > 1 && 4 * f[#f~, 1] <= k, for(i = 1, #f~, pm = max(pm, f[i, 1]^f[i, 2])); pm == f[#f~, 1], 0);} \\ _Amiram Eldar_, May 23 2024
%Y A122146 Cf. A006530, A034699, A122144, A122145.
%K A122146 nonn
%O A122146 1,1
%A A122146 Douglas Stones (dssto1(AT)student.monash.edu.au), Aug 22 2006
%E A122146 Edited by _Ray Chandler_, Aug 23 2006