login
A359563
Odd numbers that have at least two divisors with the same value of the Euler totient function (A000010).
7
63, 189, 273, 315, 441, 513, 567, 585, 693, 819, 825, 945, 1071, 1197, 1323, 1365, 1449, 1539, 1575, 1701, 1755, 1827, 1911, 1953, 2079, 2107, 2109, 2205, 2255, 2331, 2457, 2475, 2565, 2583, 2709, 2835, 2925, 2961, 3003, 3069, 3075, 3087, 3213, 3339, 3465, 3549
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
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
Complement of A326835 within the odd numbers.
Sequence in context: A077263 A098140 A008895 * A008874 A045112 A255568
KEYWORD
nonn
AUTHOR
Amiram Eldar, Jan 06 2023
STATUS
approved