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%I #23 Dec 08 2019 12:25:25
%S 180,240,360,420,480,540,600,660,780,840,1080,1320,1560,1890,1920,
%T 2016,2040,2184,2280,2352,2376,2688,2760,2856,3000,3192,3360,3480,
%U 3720,3744,4284,4320,4440,4680,4704,4896,4920,5160,5292,5640,5796,6048,6360,6552,7080,7128
%N Numbers n having a proper divisor d such that sigma(n) - k*d = k*n. Case k = 3.
%C Case k=2 are the admirable numbers (A111592).
%C Subset of A023197, A068403, A068545, A204828, A204830.
%H Amiram Eldar, <a href="/A291457/b291457.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1500 from Paolo P. Lava)
%e One of the proper divisors of 1080 is 120 and sigma(1080) - 3*120 = 3600 - 360 = 3240 = 3*1080.
%e One of the proper divisors of 17850 is 6 and sigma(17850) - 3*6 = 53568 - 18 = 53550 = 3*17850.
%p with(numtheory): P:=proc(q,h) local a,b,c,k; c:=0; a:=sort([op(divisors(q))]); for k from 1 to nops(a)-1 do if sigma(q)-h*a[k]=h*q then c:=1; break; fi; od; if c=1 then q; fi; end: seq(P(i,3),i=1..7200);
%t k=3; Select[Range[7128], (t = DivisorSigma[1, #]/k - #; # > t > 0 && IntegerQ[t] && Mod[#, t] == 0) &] (* _Giovanni Resta_, Aug 25 2017 *)
%Y Cf. A000203, A023197, A068403, A068545, A111592, A204828, A204830, A291458, A291459.
%K nonn,easy
%O 1,1
%A _Paolo P. Lava_, Aug 24 2017
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