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A336745
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Numbers m that divide the product phi(m) * sigma(m) * tau(m), where phi is the Euler totient function (A000010), sigma is the sum of divisors function (A000203) and tau is the number of divisors function (A000005).
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3
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1, 2, 6, 8, 9, 12, 18, 24, 28, 32, 36, 40, 54, 72, 80, 84, 96, 108, 117, 120, 128, 135, 144, 162, 196, 200, 216, 224, 234, 240, 243, 252, 270, 288, 324, 360, 384, 400, 405, 448, 468, 486, 496, 512, 540, 576, 588, 600, 625, 640, 648, 672, 675, 720, 756, 768, 775, 810, 819
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OFFSET
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1,2
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COMMENTS
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If s and t are terms with gcd(s, t) = 1, then s*t is another term as phi, sigma and tau are multiplicative functions.
The only prime term is 2 because prime p must divide 2*(p-1)*(p+1) to be a term.
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LINKS
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EXAMPLE
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For 24, phi(24) = 8, sigma(24) = 60 and tau(24) = 8, then 8*60*8 / 24 = 160, hence 24 is a term.
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MAPLE
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with(numtheory):
filter:= m -> irem(tau(m)*phi(m)*sigma(m), m) =0:
select(filter, [$1..850]);
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MATHEMATICA
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Select[Range[1000], Divisible[Times @@ DivisorSigma[{0, 1}, #] * EulerPhi[#], #] &] (* Amiram Eldar, Aug 02 2020 *)
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PROG
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(PARI) isok(m) = !(eulerphi(m)*sigma(m)*numdiv(m) % m); \\ Michel Marcus, Aug 05 2020
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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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