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A173745
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Numbers n such that tau(phi(n)) = sigma(rad(n)).
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1
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1, 8, 9, 25, 49, 216, 288, 324, 675, 1125, 1331, 1458, 1568, 2000, 2744, 3200, 3645, 6125, 6144, 8575, 9604, 9801, 14336, 30976, 31250, 42592, 46875, 70304, 72171, 81000, 108000, 109375, 123201, 129600, 131769, 135000, 145800, 182250, 184832
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OFFSET
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1,2
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COMMENTS
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LINKS
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FORMULA
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EXAMPLE
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For n=9, tau(phi(9)) = tau(6)=4 equals sigma(rad(9)) = sigma(3) = 4 which adds n=9 to the sequence.
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MAPLE
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with(numtheory):for n from 1 to 1500000 do : t1:= ifactors(n)[2] : t2 :=mul(t1[i][1], i=1..nops(t1)): if tau(phi(n)) = sigma(t2) then print (n): else fi: od :
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MATHEMATICA
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Select[Range[200000], DivisorSigma[0, EulerPhi[#]] == DivisorSigma[1, Times @@ FactorInteger[#][[All, 1]]] & ] (* Jean-François Alcover, Sep 12 2011 *)
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PROG
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(Magma) [1] cat [m:m in [2..200000]|#Divisors(EulerPhi(m)) eq &+Divisors(&*PrimeDivisors(m))]; // Marius A. Burtea, Jul 10 2019
(PARI) isok(n) = numdiv(eulerphi(n)) == sigma(factorback(factorint(n)[, 1])); \\ Michel Marcus, 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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EXTENSIONS
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STATUS
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approved
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