OFFSET
1,1
COMMENTS
If p is a Sophie Germain prime (A005384) then m = 16*p is a term. Indeed: m' = (16*p)' = 32*p + 16 = 16*(2*p + 1) and phi(m') = phi(32*p + 16) = phi(16*(2*p + 1)) = 8*phi(2*p + 1) = 8*2*p = m for odd p. If p = 2 then m = 16*2 = 32 is a term. - Marius A. Burtea, Apr 10 2022
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..200 from Paolo P. Lava)
EXAMPLE
For k=368, k'=752 and phi(752)=368.
MAPLE
MATHEMATICA
aQ[1]=1; aQ[n_] := EulerPhi[n * Total[#2/#1 & @@@ FactorInteger[n]]] == n; Select[Range[10000], aQ] (* Amiram Eldar, Jul 11 2019 *)
PROG
(Magma) f:=func<n | n le 1 select 0 else n*(&+[Factorisation(n)[i][2] / Factorisation(n)[i][1]: i in [1..#Factorisation(n)]])>; [k:k in [2..12000]| k eq EulerPhi(Floor(f(k)))]; // Marius A. Burtea, Apr 09 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Paolo P. Lava, Mar 21 2013
STATUS
approved