A260964 - OEIS

%I #23 Nov 17 2015 09:46:56

%S 24,492,2528,3800,18416,526688,531968,1084592,27446468,1350066372,

%T 2493705728,7768292812,15595308928

%N Numbers n such that sigma(n) = (sigma(n)-n)', where sigma(n) is the sum of the divisors of n and (sigma(n)-n)' is the arithmetic derivative of the sum of aliquot parts of n.

%C a(14) > 10^11. - _Hiroaki Yamanouchi_, Sep 11 2015

%e sigma(24) - 24 = 36 and 36' = 60 = sigma(24);

%e sigma(492) - 492 = 684 and 684' = 1176 = sigma(492).

%p with(numtheory): P:=proc(q) local a,b,c,p,n; for n from 1 to q do

%p a:=(sigma(n)-n)*add(op(2,p)/op(1,p),p=ifactors((sigma(n)-n))[2]);

%p if a=sigma(n) then print(n); fi; od; end: P(10^9);

%t d[0]=d[1]=0; d[n_] := Total[n / Divide@@@ FactorInteger@ n]; Select[Range[10^5],(s = DivisorSigma[1, #]; s == d[s - #]) &] (* _Giovanni Resta_, Aug 21 2015 *)

%Y Cf. A000203, A001065, A003415.

%K nonn,more

%O 1,1

%A _Paolo P. Lava_, Aug 18 2015

%E a(9) from _Giovanni Resta_, Aug 21 2015

%E a(10)-a(13) from _Hiroaki Yamanouchi_, Sep 11 2015