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A331667
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Numbers m with a divisor d such that tau(d)^d = m.
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0
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OFFSET
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1,2
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COMMENTS
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Corresponding values of divisors d and tau(d) are 1, 2, 9, 8, 12, 18, 32, ..., and 1, 2, 3, 4, 6, 6, 6, ..., respectively.
a(8) = 2^144*3^72 = 12^72 is too large to be included in Data. - Giovanni Resta, Feb 28 2020
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LINKS
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EXAMPLE
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19683 is a term because 3^9 = 19683; 9 divides 19683, tau(9) = 3.
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MATHEMATICA
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seqQ[n_] := AnyTrue[Divisors[n], DivisorSigma[0, #]^# == n &]; Select[Range[70000], seqQ] (* Amiram Eldar, Feb 28 2020 *)
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PROG
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(Magma) [n: n in [1..100000] | #[d: d in Divisors(n) | NumberOfDivisors(d)^d eq n] ge 1]
(PARI) isok(m) = fordiv(m, d, if (numdiv(d)^d == m, return (1)); ); \\ Michel Marcus, Mar 07 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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EXTENSIONS
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STATUS
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approved
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