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Search: id:A116020
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| A116020 |
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Numbers n such that sigma(n) - phi(n) is a repdigit greater than 2. |
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+0
3
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| 4, 8, 9, 18, 25, 27, 28, 57, 62, 85, 123, 192, 218, 258, 259, 261, 322, 403, 632, 662, 693, 1127, 2195, 2218, 2321, 2658, 3548, 4577, 4763, 5597, 5603, 5921, 6662, 7421, 7697, 9617, 9683, 10721, 10877, 11537, 12317, 13323, 17243, 18659, 23363, 26483
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OFFSET
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1,1
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COMMENT
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For every prime p sigma(p)-phi(p) is 2, so that case is trivial.
(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 (mymontain(AT)yahoo.com), Aug 24 2006
(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 (mymontain(AT)yahoo.com), Aug 24 2006
(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 (mymontain(AT)yahoo.com), Aug 24 2006
(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 (mymontain(AT)yahoo.com), Aug 24 2006
(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 (mymontain(AT)yahoo.com), Aug 24 2006
(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 (mymontain(AT)yahoo.com), Aug 24 2006
(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 (mymontain(AT)yahoo.com), Aug 24 2006
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EXAMPLE
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sigma(662) - phi(662) = 666.
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CROSSREFS
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Cf. A116017, A116018, A116019.
Sequence in context: A071592 A089765 A116030 this_sequence A064393 A035326 A063907
Adjacent sequences: A116017 A116018 A116019 this_sequence A116021 A116022 A116023
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KEYWORD
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nonn,base
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AUTHOR
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Giovanni Resta (g.resta(AT)iit.cnr.it), Feb 13 2006
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