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A116019
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Numbers n such that sigma(n) + phi(n) is a repdigit.
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2
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1, 2, 3, 4, 10, 11, 21, 49, 186, 207, 221, 342, 406, 3324, 4443, 33324, 43375, 222221, 314000, 344032, 389924, 414806, 987652, 2222221, 190476186, 222087442, 222222221, 422720878, 2222222221, 4444444443
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| (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 (mymontain(AT)yahoo.com), Aug 17 2006
(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 (mymontain(AT)yahoo.com), Aug 17 2006
(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 (mymontain(AT)yahoo.com), Aug 17 2006
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EXAMPLE
| sigma(314000)+phi(314000)=888888.
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MATHEMATICA
| Do[If[Length[Union[IntegerDigits[EulerPhi[n] + DivisorSigma[1, n]]]]==1, Print[n]], {n, 280000000}] - Farideh Firoozbakht (mymontain(AT)yahoo.com), Aug 17 2006
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CROSSREFS
| Cf. A116017, A116018, A116020.
Sequence in context: A039002 A120023 A115897 * A087460 A082866 A085701
Adjacent sequences: A116016 A116017 A116018 * A116020 A116021 A116022
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KEYWORD
| nonn,base
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AUTHOR
| Giovanni Resta (g.resta(AT)iit.cnr.it), Feb 13 2006
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EXTENSIONS
| 3 more terms from Farideh Firoozbakht (mymontain(AT)yahoo.com), Aug 17 2006
a(28)-a(30) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Jan 16 2012
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