OFFSET
1,1
COMMENTS
The even numbers are excluded from this sequence since every even number has this property: it is divisible by 1 and 2, and phi(1) = phi(2) = 1.
If k is a term then all the odd multiples of k are terms. The primitive terms are in A359564.
The numbers of terms below 10^k, for k = 1, 2, ..., are 0, 1, 12, 140, 1402, 14193, 142606, 1427749, 14283236, 142855925, ... . Apparently, the asymptotic density of this sequence exists and equals 0.01428... .
The least term that is not divisible by 3 is a(26) = 2107.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
63 is a term since it is odd, 7 and 9 are both divisors of 63, and phi(7) = phi(9) = 6.
MATHEMATICA
Select[Range[1, 3500, 2], !UnsameQ @@ EulerPhi[Divisors[#]] &]
PROG
(PARI) is(k) = k>1 && k%2 && numdiv(k) > #Set(apply(x->eulerphi(x), divisors(k)));
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Jan 06 2023
STATUS
approved