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

1,2

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

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 &]

Prog

(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); }

Crossrefs

Intersection of A025487 and A374904.

Cf. A374902, A374903.

Sequence in context: A291781 A348342 A348273 * A253122 A239413 A351893

Adjacent sequences: A374902 A374903 A374904 * A374906 A374907 A374908

Keyword

nonn

Author

Amiram Eldar, Jul 23 2024

Status

approved