A374905 Least integers of their prime signature (A025487) whose divisors have an integer mean number of divisors.

1, 4, 12, 16, 36, 64, 72, 144, 180, 192, 256, 288, 576, 720, 900, 960, 1024, 1152, 1260, 1296, 1728, 1800, 2304, 2880, 3072, 3600, 4096, 4608, 5184, 6300, 7200, 8640, 9216, 10800, 11520, 12600, 14400, 15552, 16384, 18432, 20160, 20736, 25200, 25920, 27648, 28800

Offset: 1

Author

Amiram Eldar, Jul 23 2024

Keywords

• nonn

Comments

If k is a term then every number with the same prime signature as k is a term of A374904.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A025487 and A374904.

Cf. A374902, A374903.

Programs

Mathematica

lps = Cases[Import["https://oeis.org/A025487/b025487.txt", "Table"], {, }][[;; , 2]]; f[p_, e_] := e/2 + 1; d[1] = 1; d[n_] := Denominator[Plus @@ f @@@ FactorInteger[n]]; Select[lps, d[#] == 1 &]

PARI

is(n) = {my(f = factor(n), p = f[, 1], e = f[, 2]); n == 1 || (prime(#p) == p[#p] && e == vecsort(e, , 4) && denominator(vecprod(apply(x -> x/2 +1, e))) == 1);}