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%I #5 Mar 30 2012 17:40:36
%S 4,8,9,18,25,27,28,57,62,85,123,192,218,258,259,261,322,403,632,662,
%T 693,1127,2195,2218,2321,2658,3548,4577,4763,5597,5603,5921,6662,7421,
%U 7697,9617,9683,10721,10877,11537,12317,13323,17243,18659,23363,26483
%N Numbers n such that sigma(n) - phi(n) is a repdigit greater than 2.
%C For every prime p sigma(p)-phi(p) is 2, so that case is trivial.
%C (I). If both numbers p=4*10^n+1 & q=(4*10^n-13)/9 are primes then m=p*q is in the sequence because sigma(m)-phi(m)=8*(10^(n+1)-1)/9 is a repdigit number. Conjecture: 123, 17243 & 1772443 are all such terms. - _Farideh Firoozbakht_, Aug 24 2006
%C (II). If p=(10^n-7)/3 is prime then m=2p is in the sequence because sigma(m)-phi(m)=2p+4=6*(10^n-1)/9 is a repdigit number. 62 is the smallest such terms. - _Farideh Firoozbakht_, Aug 24 2006
%C (III). If p=(4*10^n-31)/9 is prime then m=3p is in the sequence because sigma(m)-phi(m)=2p+6=8*(10^n-1)/9 is a repdigit number. 123 is the smallest such terms. - _Farideh Firoozbakht_, Aug 24 2006
%C (IV). If p=(8*10^n-17)/9 is a prime then both numbers 4p & 46p are in the sequence because sigma(4p)-phi(4p)=5p+9=4*(10^(n+1)-1)/9 & sigma(46p)-phi(46p)=50p+94=4*(10^(n+2)-1)/9 are repdigit numbers. 28 & 322 are the smallest such terms. - _Farideh Firoozbakht_, Aug 24 2006
%C (V). If p=(4*10^n-13)/9 is a prime greater than 3 then m=6p is in the sequence because sigma(m)-phi(m)=10p+14=4*(10^(n+1)-1)/9 is a repdigit number. 258 is the smallest such terms. - _Farideh Firoozbakht_, Aug 24 2006
%C (VI). If p=(8*10^(2n+1)-179)/99 is prime then m=8p is in the sequence because sigma(m)-phi(m)=11p+19=8*(10^(2n+1)-1)/9 is a repdigit number. 632 is the smallest such terms. - _Farideh Firoozbakht_, Aug 24 2006
%C (VII). If p=(10^(3n+1)-37)/27 is prime then m=12p is in the sequence because sigma(m)-phi(m)=24p+32=8*(10^(3n+1)-1)/9 is a repdigit number. 4444444428 is the smallest such terms. - _Farideh Firoozbakht_, Aug 24 2006
%e sigma(662) - phi(662) = 666.
%Y Cf. A116017, A116018, A116019.
%K nonn,base
%O 1,1
%A _Giovanni Resta_, Feb 13 2006