A291051 -id:A291051 - cp's OEIS frontend

A292390 Numbers n such that psi(n) = 2*phi(n).

3, 9, 27, 35, 81, 175, 243, 245, 729, 875, 1045, 1225, 1715, 2187, 4375, 5225, 6125, 6561, 8575, 11495, 12005, 19683, 19855, 21875, 24871, 26125, 29029, 30625, 42875, 50065, 57475, 58435, 59049, 60025, 64285, 84035, 87685, 99275, 109375, 126445, 130625, 137885, 140335, 153125

Offset: 1

Robert G. Wilson v, Amiram Eldar and Altug Alkan, Sep 15 2017

Squarefree terms are 3, 35, 1045, 24871, 29029, 50065, 58435, 64285, ... Squarefree terms of this sequence are in A062699. Note that A062699 also has terms that are not squarefree: 2011009, 3189625, 3722875, ...
If n is in the sequence, then so are all numbers that have the same set of prime factors as n. - Robert Israel, Sep 15 2017
All terms are odd. Terms divisible by 3 are powers of 3. - Robert Israel, Sep 18 2017

			3^k is a term for all k > 0 since psi(3^k) = 4*3^(k-1) = 2*phi(3^k).

Robert Israel, Table of n, a(n) for n = 1..400

Cf. A000010, A001615, A062699, A291051, A291932.

pp:= n -> mul((p+1)/(p-1), p = numtheory:-factorset(n)):
select(pp=2, [seq(i,i=1..200000,2)]); # Robert Israel, Sep 15 2017

psi[n_] := n*Sum[MoebiusMu[d]^2/d, {d, Divisors@n}]; Select[ Range@ 200000, 2EulerPhi[#] == psi[#] &]

a001615(n) = my(f=factor(n)); prod(i=1, #f~, f[i, 1]^f[i, 2] + f[i, 1]^(f[i, 2]-1));
isok(n) = a001615(n)==2*eulerphi(n); \\ after Charles R Greathouse IV at A001615

cp's OEIS Frontend

A292390 Numbers n such that psi(n) = 2*phi(n).

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