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 A244439 Numbers n such that phi(n)*sigma(n) = phi(n+1)*sigma(n+1). 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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 LINKS Giovanni Resta, Table of n, a(n) for n = 1..52 (terms < 10^13, first 40 terms from Jens Kruse Andersen) EXAMPLE 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. MAPLE with(numtheory): A244439:=n->`if`(phi(n)*sigma(n) = phi(n+1)*sigma(n+1), n, NULL): seq(A244439(n), n=1..10^4); # Wesley Ivan Hurt, Aug 16 2014 MATHEMATICA Select[Range[10^5], Equal @@ (EulerPhi[{#, # + 1}] DivisorSigma[1, {#, # + 1}]) &] (* Giovanni Resta, Jun 08 2020 *) PROG (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 CROSSREFS Cf. A000010, A000203, A145749. Sequence in context: A129420 A247711 A284066 * A216446 A307991 A015221 Adjacent sequences:  A244436 A244437 A244438 * A244440 A244441 A244442 KEYWORD nonn AUTHOR Farideh Firoozbakht, Aug 14 2014 EXTENSIONS More terms from Jens Kruse Andersen, Aug 16 2014 STATUS approved

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Last modified April 20 01:20 EDT 2021. Contains 343117 sequences. (Running on oeis4.)