1,2

(1). If p=(10^(3n+2)-19)/27 is a prime greater than 3 then m=6p is in the sequence because m+sigma(m)=6*(10^(3n+2)-1)/9 (the proof is easy), so m+sigma(m) is a repdigit number. The smallest such terms is 22222218, the next such term is 6*(10^(3*430+2)-1)/9=222...218 which has 1292 digits. - Farideh Firoozbakht (mymontain(AT)yahoo.com), Aug 17 2006

(2). If p=5*10^n-1 is prime then p is in the sequence because p+sigma(p)=10^(n+1)-1, so p+sigma(p) is a repdigit number. 499, 49999, 4999999,... are such terms. - Farideh Firoozbakht (mymontain(AT)yahoo.com), Aug 17 2006

(3). If p=(25*10^(n-1)-7)/9 is prime then p is in the sequence because p+sigma(p)=5*(10^n-1)/9, so p+sigma(p) is a repdigit number. 2, 277, 2777, 2777777777, ... are such terms. - Farideh Firoozbakht (mymontain(AT)yahoo.com), Aug 17 2006

(4). If p=(16*10^(n-1)-7)/9 is prime then m=2p is in the sequence because m+sigma(m)=8*(10^n-1) /9, so m+sigma(m) is a repdigit number. 34, 3554, 3555555554, ... are such terms. - Farideh Firoozbakht (m\ ymontain(AT)yahoo.com), Aug 17 2006, Dec 08 2007

22222218+sigma(22222218)=66666666.

Do[If[Length[Union[IntegerDigits[n + DivisorSigma[1, n]]]]==1, Print[n]], {n, 60000000}] - Farideh Firoozbakht (mymontain(AT)yahoo.com), Aug 17 2006

Cf. A116018.

Sequence in context: A065885 A092233 A115895 this_sequence A067033 A067034 A039697

Adjacent sequences: A116014 A116015 A116016 this_sequence A116018 A116019 A116020

nonn,base

Giovanni Resta (g.resta(AT)iit.cnr.it), Feb 13 2006

One more term from Farideh Firoozbakht (mymontain(AT)yahoo.com), Aug 17 2006

More terms from Farideh Firoozbakht (mymontain(AT)yahoo.com), Dec 19 2007