A329878 Numbers k such that k and psi(k) have the same set of prime divisors, where psi is the Dedekind psi function (A001615).

1, 6, 12, 18, 24, 36, 48, 54, 72, 96, 108, 144, 150, 162, 192, 216, 288, 294, 300, 324, 384, 432, 450, 486, 576, 588, 600, 648, 726, 750, 768, 864, 882, 900, 972, 1152, 1176, 1200, 1296, 1350, 1452, 1458, 1500, 1536, 1728, 1734, 1764, 1800, 1944, 2058, 2178

Offset

1,2

Comments

Numbers k such that rad(psi(k)) = rad(k), where rad(k) is the squarefree kernel of k (A007947).

Links

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

Example

6 is in the sequence since 6 = 2 * 3 and psi(6) = 12 = 2^2 * 3 have the same set of prime divisors, {2, 3}.

Mathematica

rad[n_] := Times @@ (First@# & /@ FactorInteger@ n); psi[1] = 1; psi[n_] := n * Times @@ (1 + 1/Transpose[FactorInteger[n]][[1]]); Select[Range[2000], rad[psi[#]] == rad[#] &]

Crossrefs

Cf. A001615, A007947, A027598, A055744.

Sequence in context: A358757 A353530 A244193 * A215142 A033845 A187778

Adjacent sequences: A329875 A329876 A329877 * A329879 A329880 A329881

Keyword

nonn

Author

Amiram Eldar, Nov 23 2019

Status

approved