A374906 a(n) is the least number whose divisors have a mean number of divisors that equals n.

1, 4, 12, 36, 72, 144, 288, 576, 720, 1728, 4608, 2880, 18432, 7200, 8640, 14400, 294912, 20160, 1179648, 43200, 50400, 115200, 18874368, 100800, 172800, 460800, 181440, 352800, 1207959552, 302400, 4831838208, 705600, 806400, 7372800, 1058400, 907200, 309237645312

Offset: 1

Author

Amiram Eldar, Jul 23 2024

Keywords

• nonn

Comments

a(n) is the least number k such that A374902(k)/A374903(k) = A007425(k)/A000005(k) = n.

All the terms are in A025487.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000005, A005179, A007425, A025487, A374902, A374903, A374904, A374905, A374907.

Programs

Mathematica

lps = Cases[Import["https://oeis.org/A025487/b025487.txt", "Table"], {, }][[;; , 2]]; f[p_, e_] := e/2 + 1; f[1] = 1; f[n_] := Times @@ f @@@ FactorInteger[n]; s = f /@ lps; lps[[TakeWhile[Flatten[FirstPosition[s, #] & /@ Range[Max[s]]], ! MissingQ[#] &]]]

Formula

a(p) = 9 * 2^(p-2) for prime p >= 5.

a(p^e) = 9 * 2^(p^e-2) for prime p >= 3 and e >= 2.