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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
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
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
KEYWORD
nonn
AUTHOR
Amiram Eldar, Nov 23 2019
STATUS
approved