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%I #22 Sep 08 2022 08:46:25
%S 1,4,19683,65536,2176782336,101559956668416,7958661109946400884391936
%N Numbers m with a divisor d such that tau(d)^d = m.
%C 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.
%C a(8) = 2^144*3^72 = 12^72 is too large to be included in Data. - _Giovanni Resta_, Feb 28 2020
%e 19683 is a term because 3^9 = 19683; 9 divides 19683, tau(9) = 3.
%t seqQ[n_] := AnyTrue[Divisors[n], DivisorSigma[0, #]^# == n &]; Select[Range[70000], seqQ] (* _Amiram Eldar_, Feb 28 2020 *)
%o (Magma) [n: n in [1..100000] | #[d: d in Divisors(n) | NumberOfDivisors(d)^d eq n] ge 1]
%o (PARI) isok(m) = fordiv(m, d, if (numdiv(d)^d == m, return (1));); \\ _Michel Marcus_, Mar 07 2020
%Y Cf. A236284 (tau(n)^n).
%Y Cf. A000005, A332646.
%K nonn
%O 1,2
%A _Jaroslav Krizek_, Feb 28 2020
%E More terms from _Giovanni Resta_, Feb 28 2020
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