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%I #14 Aug 25 2017 03:54:13
%S 294053760,575134560,739458720,882161280,1193512320,1314593280,
%T 1725403680,2539555200,2588105520,2646483840,2711348640,3008396160,
%U 3891888000,4053329280,4214770560,4648644000,4802878080,5176211040,5194949760,5258373120,6470263800,6768891360,7900532640
%N Numbers n having a proper divisor d such that sigma(n) - k*d = k*n. Case k = 5.
%C Case k=2 are the admirable numbers (A111592).
%C Subset of A215264.
%e One of the proper divisors of 294053760 is 2056320 and sigma(294053760) - 5*2056320 = 1480550400 - 10281600 = 1470268800 = 5*294053760.
%e One of the proper divisors of 3891888000 is 314496 and sigma(3891888000) - 5*314496 = 19461012480 - 1572480 = 19459440000 = 5*3891888000.
%p with(numtheory): P:=proc(q,h) local a,k,n; for n from 1 to q do a:=sort([op(divisors(n))]);
%p for k from 1 to nops(a)-1 do if sigma(n)-h*a[k]=h*n then print(n); break; fi; od; od; end: P(10^10,5);
%Y Cf. A000203, A111592, A215264, A291457, A291458.
%K nonn,easy
%O 1,1
%A _Paolo P. Lava_, Aug 24 2017
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