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

1,1

Comments

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

Links

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

Example

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

Maple

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

Mathematica

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

Prog

(PARI) 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

Crossrefs

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

Sequence in context: A070364 A070363 A305617 * A211219 A248959 A070362

Adjacent sequences: A292387 A292388 A292389 * A292391 A292392 A292393

Keyword

nonn,easy

Author

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

Status

approved