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A173617
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Numbers n such that phi(tau(n))= rad(n)
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0
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1, 4, 8, 32, 36, 192, 288, 768, 972, 1458, 5120, 13122, 326592, 19531250, 22588608, 46137344, 171532242
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OFFSET
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1,2
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COMMENTS
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rad(n) is the product of the primes dividing n (A007947 ) tau(n) is the number of divisors of n (A000005) phi(n): Euler totient function (A000010)
a(18) > 10^10. - Donovan Johnson, Jul 27 2011
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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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tau(8) = 4, phi(4)=2 and rad(8)=2 tau(13122) = 18, phi(18)=6 and rad(13122)=6
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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(tau(n)) = t2 then print (n): else fi : od :
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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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