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Numbers k such that k + sigma(k) + sigma(sigma(k)) is a repdigit.
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%I #11 Jul 15 2021 06:39:20

%S 1,2,15,25,119,157,2413,2623,8415,14962,18303,66078,1031747,62826675,

%T 692799137,759500195,1144100379

%N Numbers k such that k + sigma(k) + sigma(sigma(k)) is a repdigit.

%C a(18) > 5*10^9. - _Donovan Johnson_, Feb 18 2013

%e 1031747 + sigma(1031747) + sigma(sigma(1031747)) = 5555555.

%t repQ[n_]:=Module[{ds=DivisorSigma[1,n]},Count[DigitCount[n+ds+ DivisorSigma[ 1,ds]],0] == 9]; Select[Range[66100],repQ] (* The program generates the first 12 terms of the sequence. To generate more, increase the Range constant, but it will take a long time to run. *) (* _Harvey P. Dale_, Oct 08 2020 *)

%Y Cf. A010785, A116017.

%K nonn,base

%O 1,2

%A _Giovanni Resta_, Feb 13 2006

%E a(14)-a(17) from _Donovan Johnson_, Feb 18 2013