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A172464 Numbers n such that phi(phi(n)) + sigma(sigma(n)) is a 4th power. 1
9, 42, 101, 339, 407, 420, 471, 915, 1409, 2572, 2847, 3706, 4069, 6631, 6720, 7229, 9212, 14051, 16641, 31453, 33067, 33146, 35701, 37425, 37675, 37911, 48016, 48272, 53101, 55956, 56906, 68895, 73474, 75023, 83525, 84676, 86928, 94525, 101428, 101743, 115925 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
REFERENCES
W. L. Glaisher, Number-Divisor Tables. British Assoc. Math. Tables, Vol. 8, Camb. Univ. Press, 1940, p. 64.
S. W. Golomb, Equality among number-theoretic functions, Abstract 882-11-16, Abstracts Amer. Math. Soc., 14 (1993), 415-416.
R. K. Guy, Unsolved Problems in Number Theory, B42.
LINKS
K. Ford, The distribution of totients, Electron. Res. Announc. Amer. Math. Soc. 4 (1998), 27-34.
Eric Weisstein's World of Mathematics, Totient Valence Function
Eric Weisstein's World of Mathematics, Carmichael's Totient Function conjecture
EXAMPLE
phi(phi(9)) + sigma(sigma(9))= 1;
phi(phi(42)) + sigma(sigma(42))= 4^4 = 256;
phi(phi(101)) + sigma(sigma(101))= 4^4 = 256;
phi(phi(339)) + sigma(sigma(339))= 6^4 = 1296.
MAPLE
with(numtheory): for n from 1 to 2000000 do; if floor(( phi(phi(n)) + sigma(sigma(n)))^.25) =( phi(phi(n)) + sigma(sigma(n)))^.25 then print (n); fi ; od;
MATHEMATICA
Select[Range[116000], IntegerQ[Surd[DivisorSigma[1, DivisorSigma[1, #]]+ EulerPhi[ EulerPhi[ #]], 4]]&] (* Harvey P. Dale, Aug 16 2021 *)
CROSSREFS
Sequence in context: A336984 A075233 A062783 * A269053 A027441 A000971
KEYWORD
nonn
AUTHOR
Michel Lagneau, Feb 03 2010
EXTENSIONS
a(40)-a(41) from Hiroaki Yamanouchi, Sep 19 2014
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)