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

1,2

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

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.

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[#] &]]]

Crossrefs

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

Sequence in context: A095735 A020875 A307182 * A357061 A190072 A063810

Adjacent sequences: A374903 A374904 A374905 * A374907 A374908 A374909

Keyword

nonn

Author

Amiram Eldar, Jul 23 2024

Status

approved