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A292390
Numbers n such that psi(n) = 2*phi(n).
1
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
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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved