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A244439
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Numbers n such that phi(n)*sigma(n) = phi(n+1)*sigma(n+1).
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2
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5, 55, 56, 123, 135, 147, 175, 304, 351, 644, 1015, 2464, 19304, 61131, 162524, 476671, 567644, 712724, 801944, 2435488, 3346399, 3885056, 4555999, 8085560, 8369360, 12516692, 22702119, 29628800, 83884031, 83994624, 84789247, 354812535, 860616295, 1091535704
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OFFSET
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1,1
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COMMENTS
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Since both numbers 55 and 56 are in the sequence we have sigma(55)*phi(55) = sigma(56)*phi(56) = sigma(57)*phi(57). It seems that 56 is the only number n which has the nice property sigma(n-1)*phi(n-1) = sigma(n)*phi(n) = sigma(n+1)*phi(n+1).
Up to n < 6*10^11 the similar equation phi(n)*sigma(n+1) = phi(n+1)*sigma(n) is satisfied only by n = 696003. - Giovanni Resta, Jun 08 2020
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LINKS
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EXAMPLE
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5 is in the sequence because sigma(5)*phi(5) = sigma(6)*phi(6) = 24.
55 is in the sequence because sigma(55)*phi(55) = sigma(56)*phi(56) = 2880.
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MAPLE
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MATHEMATICA
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Select[Range[10^5], Equal @@ (EulerPhi[{#, # + 1}] DivisorSigma[1, {#, # + 1}]) &] (* Giovanni Resta, Jun 08 2020 *)
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PROG
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(PARI)
for(n=1, 10^6, s=eulerphi(n)*sigma(n); if(s==eulerphi(n+1)*sigma(n+1), print1(n, ", "))) \\ Derek Orr, Aug 14 2014
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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