This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A116019 #26 Aug 09 2025 21:06:21
%S A116019 1,2,3,4,10,11,21,49,186,207,221,342,406,3324,4443,33324,43375,222221,
%T A116019 314000,344032,389924,414806,987652,2222221,190476186,222087442,
%U A116019 222222221,422720878,2222222221,4444444443
%N A116019 Numbers k such that sigma(k) + phi(k) is a repdigit.
%C A116019 (1). If m=(2*10^n-11)/9 is product of two distinct primes then m is in the sequence because phi(m)+sigma(m)=phi(p*q)+sigma(p*q)=2(p*q+1)=2m+2=4*(10^n-1)/9, so phi(m)+sigma(m) is a repdigit number. 21, 221, 222221, 2222221, 222222221,... are such terms. - _Farideh Firoozbakht_, Aug 17 2006
%C A116019 (2). If m=(4*10^n-13)/9 is product of two distinct primes then m is in the sequence because phi(m)+sigma(m)=phi(p*q)+sigma(p*q)=2(p*q+1)=2m+2=8*(10^n-1)/9, so phi(m)+sigma(m) is a repdigit number. 4443, 4444444443, 44444444443,... are such terms. - _Farideh Firoozbakht_, Aug 17 2006
%C A116019 (3). If p=(25*10^(n-1)-7)/9 is an odd prime then m=12*p is in the sequence because phi(m)+sigma(m)=32p+24=8*(10^(n+1)-1)/9 so phi(m)+sigma(m) is a repdigit number. 3324, 33324, 33333333324,... are such terms. - _Farideh Firoozbakht_, Aug 17 2006
%C A116019 (4). If n is a nonnegative integer and p=(8*10^(3n+2)-17)/27 is prime then m=14*p is in the sequence because phi(m)+sigma(m)=30p+18=8*(10^(3n+3)-1)/9 is a repdigit number. 406, 414806, 414814814814814814814806, ... are such terms of the sequence. - _Farideh Firoozbakht_, Aug 01 2014
%e A116019 sigma(314000)+phi(314000)=888888.
%t A116019 Do[If[Length[Union[IntegerDigits[EulerPhi[n] + DivisorSigma[1, n]]]]==1, Print[n]], {n, 280000000}] (* _Farideh Firoozbakht_, Aug 17 2006 *)
%o A116019 (PARI)
%o A116019 for(n=1,10^7,d=digits(sigma(n)+eulerphi(n));c=0;for(i=1,#d-1,if(d[i]!=d[i+1],c++;break));if(c==0,print1(n,", "))) \\ _Derek Orr_, Aug 01 2014
%Y A116019 Cf. A116017, A116018, A116020.
%K A116019 nonn,base
%O A116019 1,2
%A A116019 _Giovanni Resta_, Feb 13 2006
%E A116019 3 more terms from _Farideh Firoozbakht_, Aug 17 2006
%E A116019 a(28)-a(30) from _Donovan Johnson_, Jan 16 2012