

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
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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S. W. Golomb, Equality among numbertheoretic functions, Unpublished manuscript.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 !! (n1)
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



