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A364977 Numbers k such that k/(3*k - sigma(k)) is a positive integer.

%I A364977 #7 Aug 15 2023 02:09:01
%S A364977 6,24,28,60,84,168,252,270,336,496,630,756,792,864,924,936,1140,1170,
%T A364977 1488,1638,2268,2808,2970,3672,4464,5148,5472,6804,7308,7644,8128,
%U A364977 8700,8910,9300,9936,11172,13392,16368,18018,20196,20412,22230,24384,25116,27888,31968
%N A364977 Numbers k such that k/(3*k - sigma(k)) is a positive integer.
%C A364977 Analogous to A271816 as 3-abundant numbers (A068403) are analogous to abundant numbers (A005101).
%C A364977 Numbers k such that the sum of the divisors of k with one of them added twice is equal to 3*k.
%C A364977 The perfect numbers (A000396) are all terms.
%C A364977 For all the terms k, 2 <= sigma(k)/k < 3, i.e., they are all nondeficient numbers (A023196), and none are 3-abundant (A068403).
%H A364977 Amiram Eldar, <a href="/A364977/b364977.txt">Table of n, a(n) for n = 1..600</a>
%e A364977 6 is a term since 3*6 - sigma(6) = 6 > 0 and 6 is divisible by 6.
%e A364977 24 is a term since 3*24 - sigma(24) = 12 > 0 and 24 is divisible by 12.
%t A364977 Select[Range[32000], (d = 3*# - DivisorSigma[1, #]) > 0 && Divisible[#, d] &]
%o A364977 (PARI) is(n) = {my(d = 3*n - sigma(n)); d > 0 && n%d == 0;}
%Y A364977 Cf. A000203 (sigma), A000396, A023196, A068403, A271816, A329189, A364976.
%K A364977 nonn
%O A364977 1,1
%A A364977 _Amiram Eldar_, Aug 15 2023