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A172464
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Numbers n such that phi(phi(n)) + sigma(sigma(n)) is a 4th power.
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1
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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
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OFFSET
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1,1
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REFERENCES
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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.
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LINKS
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EXAMPLE
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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.
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MAPLE
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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;
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MATHEMATICA
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Select[Range[116000], IntegerQ[Surd[DivisorSigma[1, DivisorSigma[1, #]]+ EulerPhi[ EulerPhi[ #]], 4]]&] (* Harvey P. Dale, Aug 16 2021 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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