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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S. W. Golomb, Equality among number-theoretic functions, Unpublished manuscript.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

Jud McCranie

STATUS

approved

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Last modified November 17 20:50 EST 2018. Contains 317278 sequences. (Running on oeis4.)