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A033632
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Numbers k such that sigma(phi(k)) = phi(sigma(k)).
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38
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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
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1,2
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COMMENTS
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The largest term of this sequence that I found is 3^9550. Also, if (1/2)*(3^(k+1)-1) is prime (k+1 is a term of A028491) then 3^k is in the sequence, namely sigma(phi(3^k) = phi(sigma(3^k)) (the proof is easy). - Farideh Firoozbakht, Feb 09 2005
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REFERENCES
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R. K. Guy, Unsolved Problems in Number Theory, 2nd edition, Springer Verlag, 1994, section B42, p. 99.
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LINKS
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FORMULA
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MATHEMATICA
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Select[ Range[ 10^6 ], DivisorSigma[ 1, EulerPhi[ # ] ] == EulerPhi[ DivisorSigma[ 1, # ] ] & ]
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PROG
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(Haskell)
a033632 n = a033632_list !! (n-1)
a033632_list = filter (\x -> a062401 x == a062402 x) [1..]
(Python)
from sympy import divisor_sigma as sigma, totient as phi
def ok(n): return sigma(phi(n)) == phi(sigma(n))
def aupto(nn): return [m for m in range(1, nn+1) if ok(m)]
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CROSSREFS
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KEYWORD
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nonn,nice
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AUTHOR
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STATUS
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approved
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