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A336354 Numbers k such that p^2 divides k, where p = A006530(k), the largest prime factor of k, and sigma(k) does not have any prime factor larger than p.

%I A336354 #18 Jul 14 2024 12:28:45
%S A336354 343,686,1029,1372,1715,2058,2744,3430,4116,4489,5145,6241,6860,8232,
%T A336354 8978,9261,10290,10976,12482,13467,13720,17956,18522,18723,18769,
%U A336354 20580,22201,22445,24964,26569,26934,31205,31423,32761,32928,35912,36481,37044,37446,37538,40401
%N A336354 Numbers k such that p^2 divides k, where p = A006530(k), the largest prime factor of k, and sigma(k) does not have any prime factor larger than p.
%H A336354 David A. Corneth, <a href="/A336354/b336354.txt">Table of n, a(n) for n = 1..10000</a>
%e A336354 343 = 7^3 is present, as A000203(343) = 400 = 2^4 * 5^2, with none of the prime factors > 7.
%e A336354 1715 = 5 * 7^3 is present, as sigma(1715) = 2400 = 2^5 * 3 * 5^2.
%o A336354 (PARI) isA336354(n) = ((0==A336352(n))&&(1==A319988(n)));
%o A336354 (PARI) is(n) = {if(n == 1, return(0));
%o A336354 	my(f = factor(n), s, fs);
%o A336354 	if(f[#f~, 2] < 2, return(0));
%o A336354 	s = sigma(f);
%o A336354 	fs = factor(s, f[#f~, 1]);
%o A336354 	fs[#fs~, 1] <= f[#f~, 1]
%o A336354 } \\ _David A. Corneth_, Jun 27 2024
%Y A336354 Intersection of A070003 and A336353.
%Y A336354 Cf. A000203, A006530, A319988, A336352.
%K A336354 nonn
%O A336354 1,1
%A A336354 _Antti Karttunen_, Jul 19 2020