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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

%I #9 Nov 25 2019 03:31:15

%S 1,6,12,18,24,36,48,54,72,96,108,144,150,162,192,216,288,294,300,324,

%T 384,432,450,486,576,588,600,648,726,750,768,864,882,900,972,1152,

%U 1176,1200,1296,1350,1452,1458,1500,1536,1728,1734,1764,1800,1944,2058,2178

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

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

%H Amiram Eldar, <a href="/A329878/b329878.txt">Table of n, a(n) for n = 1..10000</a>

%e 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}.

%t 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[#] &]

%Y Cf. A001615, A007947, A027598, A055744.

%K nonn

%O 1,2

%A _Amiram Eldar_, Nov 23 2019

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Last modified September 12 22:49 EDT 2024. Contains 375855 sequences. (Running on oeis4.)