|
%I #10 May 19 2023 06:14:39
%S 36,72,100,108,144,196,200,216,288,324,392,400,432,500,576,648,784,
%T 800,864,900,968,972,1000,1152,1296,1352,1372,1568,1600,1728,1764,
%U 1800,1936,1944,2000,2304,2500,2592,2700,2704,2744,2916,3136,3200,3456,3528,3600,3872,3888,4000
%N Powerful abundant numbers: numbers that are both powerful (A001694) and abundant (A005101).
%C The least odd term is a(90) = 11025, and the least term that is coprime to 6 is 1382511906801025.
%C Are there two consecutive integers in this sequence? There are none below 10^22.
%H Amiram Eldar, <a href="/A363169/b363169.txt">Table of n, a(n) for n = 1..10534</a> (terms not exceeding 10^8)
%e 36 = 2^2 * 3^2 is a term since it is powerful, and sigma(36) = 91 > 2*36 = 72.
%t Select[Range[4000], DivisorSigma[-1, #] > 2 && Min[FactorInteger[#][[;;, 2]]] > 1 &]
%o (PARI) is(n) = { my(f = factor(n)); n > 1 && vecmin(f[, 2]) > 1 && sigma(f, -1) > 2; }
%Y Intersection of A001694 and A005101.
%Y Cf. A180114, A363170, A363171.
%Y Subsequences: A307959, A328136, A356871.
%K nonn
%O 1,1
%A _Amiram Eldar_, May 19 2023
|
