This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A331667 #22 Sep 08 2022 08:46:25 %S A331667 1,4,19683,65536,2176782336,101559956668416,7958661109946400884391936 %N A331667 Numbers m with a divisor d such that tau(d)^d = m. %C A331667 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 A331667 a(8) = 2^144*3^72 = 12^72 is too large to be included in Data. - _Giovanni Resta_, Feb 28 2020 %e A331667 19683 is a term because 3^9 = 19683; 9 divides 19683, tau(9) = 3. %t A331667 seqQ[n_] := AnyTrue[Divisors[n], DivisorSigma[0, #]^# == n &]; Select[Range[70000], seqQ] (* _Amiram Eldar_, Feb 28 2020 *) %o A331667 (Magma) [n: n in [1..100000] | #[d: d in Divisors(n) | NumberOfDivisors(d)^d eq n] ge 1] %o A331667 (PARI) isok(m) = fordiv(m, d, if (numdiv(d)^d == m, return (1));); \\ _Michel Marcus_, Mar 07 2020 %Y A331667 Cf. A236284 (tau(n)^n). %Y A331667 Cf. A000005, A332646. %K A331667 nonn %O A331667 1,2 %A A331667 _Jaroslav Krizek_, Feb 28 2020 %E A331667 More terms from _Giovanni Resta_, Feb 28 2020