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A173748
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Numbers k such that phi(phi(k)) = sigma(rad(k)).
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1
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1, 108, 135, 196, 245, 297, 539, 810, 1008, 1176, 1575, 1782, 1917, 3056, 3213, 4464, 6897, 6944, 7560, 8820, 9450, 10017, 11502, 14229, 16632, 16821, 18009, 18336, 19278, 19404, 20320, 24255, 25400, 25823, 27504, 28677, 33250, 33480, 41382
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OFFSET
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1,2
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COMMENTS
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rad(k) is the product of the primes dividing k (A007947), phi(k) is the Euler totient function (A000010), sigma(k) is the sum of divisors of k (A000203).
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REFERENCES
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 840.
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LINKS
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FORMULA
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EXAMPLE
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for n=108,phi(108) = 36,phi(36)=12, rad(108)=6 and sigma(6) = 12
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MAPLE
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with(numtheory): for n from 1 to 1000000 do : t1:= ifactors(n)[2] : t2 :=mul(t1[i][1], i=1..nops(t1)): if phi(phi(n)) = sigma(t2)then print (n): else fi: od :
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MATHEMATICA
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Select[Range[50000], EulerPhi[EulerPhi[#]]==DivisorSigma[1, Times@@ FactorInteger[ #][[All, 1]]]&] (* Harvey P. Dale, Aug 21 2016 *)
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PROG
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(Magma) [1] cat [m:m in [2..42000]|EulerPhi((EulerPhi(m))) eq &+Divisors(&*PrimeDivisors(m))]; // Marius A. Burtea, Jul 10 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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