%I #47 Dec 07 2019 12:18:27
%S 4,5,506311,4761903,506767303,5517762660583,5554746531623,
%T 5555541480743
%N Numbers n such that n+sigma(n) is a repunit number.
%C This sequence is a subsequence of A116017.
%C a(6) > 10^11. - _Hiroaki Yamanouchi_, Aug 26 2014
%C a(9) > 10^13. The numbers 47379454926624737751 and 546139199807860751551844463475591 belong to this sequence. - _Giovanni Resta_, Aug 17 2019
%C a(9) <= 5458110152757191. Also in the sequence is 38808343270779723425176258917550576371890625326889683884600092615. - _Daniel Suteu_, Aug 23 2019
%e sigma(4761903)+4761903 = 11111111.
%o (PARI)
%o for(n=1, 10^10, d=digits(sigma(n)+n); if(vecmax(d)==1&&vecmin(d)==1, print1(n, ", "))) \\ _Derek Orr_, Aug 02 2014
%o (Python) from sympy import divisors
%o [n for n in range(1,10**6) if len(set(str(n+sum(divisors(n))))) == 1 and str(n+sum(divisors(n)))[0] == '1'] # _Chai Wah Wu_, Aug 04 2014
%Y Cf. A116017, A309835.
%K nonn,base,more,hard
%O 1,1
%A _Farideh Firoozbakht_, Aug 01 2014
%E a(5) from _Hiroaki Yamanouchi_, Aug 26 2014
%E a(6)-a(8) from _Giovanni Resta_, Aug 17 2019