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Numbers k such that A187795(k) > 2*k.
4

%I #11 Sep 20 2021 18:29:25

%S 60,72,108,120,144,168,180,216,240,252,264,280,288,300,312,324,336,

%T 360,396,400,420,432,468,480,504,528,540,560,576,588,600,612,624,648,

%U 660,672,684,720,756,780,792,800,816,828,840,864,880,900,912,924,936,960,972

%N Numbers k such that A187795(k) > 2*k.

%C Numbers k whose sum of aliquot divisors that are abundant numbers is > k.

%C If k is a term then all the positive multiples of k are also terms.

%C The smallest odd term is a(10042) = 155925.

%C The numbers of terms not exceeding 10^k for k = 1, 2, ... are 0, 2, 53, 629, 6423, 63932, 639947, 6395539, 63934596, ... Apparently, this sequence has an asymptotic density 0.0639...

%H Amiram Eldar, <a href="/A347935/b347935.txt">Table of n, a(n) for n = 1..10000</a>

%e The divisors of 60 are {1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60}. The abundant divisors are {12, 20, 30, 60} and their sum is 122 > 2*60 = 120. Therefore, 60 is a term.

%t abQ[n_] := DivisorSigma[1, n] > 2*n; s[n_] := DivisorSum[n, # &, abQ[#] &]; q[n_] := s[n] > 2*n; Select[Range[1000], q]

%o (PARI) isok(k) = sumdiv(k, d, if (sigma(d)>2*d, d)) > 2*k; \\ _Michel Marcus_, Sep 20 2021

%Y Subsequence of A005101.

%Y Cf. A187795.

%K nonn

%O 1,1

%A _Amiram Eldar_, Sep 20 2021