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 A033632 Numbers n such that sigma(phi(n)) = phi(sigma(n)). 34
 1, 9, 225, 242, 516, 729, 3872, 13932, 14406, 17672, 18225, 20124, 21780, 29262, 29616, 45996, 65025, 76832, 92778, 95916, 106092, 106308, 114630, 114930, 121872, 125652, 140130, 140625, 145794, 149124, 160986, 179562, 185100, 234876, 248652, 252978, 256860 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The largest term of this sequence that I found is 3^9550. Also, if (1/2)*(3^(n+1)-1) is prime (n+1 is a term of A028491) then 3^n is in the sequence, namely sigma(phi(3^n) = phi(sigma(3^n)) (the proof is easy). - Farideh Firoozbakht, Feb 09 2005 REFERENCES R. K. Guy, Unsolved Problems in Number Theory, 2nd edition, Springer Verlag, 1994, section B42, p.99. LINKS T. D. Noe and Donovan Johnson, Table of n, a(n) for n = 1..10000 (first 200 terms from T. D. Noe) S. W. Golomb, Equality among number-theoretic functions, Unpublished manuscript. (Annotated scanned copy) Walter Nissen, sigma(phi(n)) = phi(sigma(n)), Up for the Count ! Walter Nissen, sigma(phi(n)) = phi(sigma(n)): From "5" to "5 figures", Up for the Count !, Nov. 14, 2000 Walter Nissen, Addendum to : sigma(phi()): From "5" to "5 figures", Up for the Count !, June 8, 2008 Walter Nissen, Elaboration of : sigma(phi()): From "5" to "5 figures", Up for the Count !, Oct. 15, 2010 FORMULA A062401(a(n)) = A062402(a(n)). - Reinhard Zumkeller, Jan 04 2013 MAPLE with(numtheory); P:=proc(q) local n; for n from 1 to q do if sigma(phi(n))=phi(sigma(n)) then print(n); fi; od; end: P(10^6); # Paolo P. Lava, Aug 08 2013 MATHEMATICA Select[ Range[ 10^6 ], DivisorSigma[ 1, EulerPhi[ # ] ] == EulerPhi[ DivisorSigma[ 1, # ] ] & ] PROG (Haskell) a033632 n = a033632_list !! (n-1) a033632_list = filter (\x -> a062401 x == a062402 x) [1..] -- Reinhard Zumkeller, Jan 04 2013 (PARI) is(n)=sigma(eulerphi(n))==eulerphi(sigma(n)) \\ Charles R Greathouse IV, May 09 2013 CROSSREFS Cf. A000203, A000010, A028491, A078148. Sequence in context: A221439 A205568 A264848 * A110260 A036896 A120319 Adjacent sequences:  A033629 A033630 A033631 * A033633 A033634 A033635 KEYWORD nonn,nice AUTHOR STATUS approved

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Last modified October 15 20:04 EDT 2019. Contains 328037 sequences. (Running on oeis4.)