A374907 -id:A374907 - cp's OEIS frontend

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

Amiram Eldar, Jul 23 2024

nonn

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

All the terms are in A025487.

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

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

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[#] &]]]

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.

cp's OEIS Frontend

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

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