A193987 Least number k such that tau(tau(k)) = n.

1, 2, 6, 12, 120, 60, 7560, 360, 1260, 2520, 294053760, 5040, 128501493120, 332640, 110880, 55440, 106858629141264000, 277200, 188391763176048432000, 720720, 21621600, 27935107200, 1356699703068812438127792000, 3603600, 857656800, 18632716502400, 227026800, 183783600

Offset: 1

Author

T. D. Noe, Aug 10 2011

Keywords

• nonn

Comments

Here tau is the number of divisors function, A000005. Such a k always exists because an upper bound is 2^(2^n-1). For n < 19, and small composite numbers, terms can be found among the highly composite numbers, A002182. The b-file in A005179 is useful when tau^(-1)(n) is small.

Crossrefs

Cf. A010553 (tau(tau(n))), A000005, A002182, A005179.

Extensions

a(27) corrected by Amiram Eldar, Jan 20 2025