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

Author

Amiram Eldar, Nov 23 2019

Keywords

• nonn

Comments

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

Examples

			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}.
		

Links

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

Crossrefs

Cf. A001615, A007947, A027598, A055744.

Programs

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[#] &]