A329872 Nontotients (A005277) that are the product of two totients (A002202).

484, 968, 1100, 2116, 3364, 4232, 6084, 6724, 6728, 8464, 10404, 11132, 11236, 13448, 16928, 19044, 22472, 26896, 27556, 29584, 31684, 36100, 44944, 51076, 53792, 55112, 56644, 59168, 63368, 65824, 67416, 68644, 72200, 79524, 80344, 89888, 96100, 99856, 102152, 107584

Offset: 1

Author

Jianing Song, Nov 23 2019

Keywords

• nonn

Comments

We can have a list of nontotients and their factorizations into two totients. A totient m is in A301587 if and only if m never occurs in this list as a divisor of the nontotients. Using the list, many totients (10, 22, 44, 46, ...) are ruled out of A301587. But generally it's hard to prove that a number is in A301587.

Examples

			484 is here, because 484 = 22*22, and 22 is a totient while 484 isn't. Similarly, if p == 3 (mod 4) is a prime such that (p-1)^2+1 is composite, then (p-1)^2 is here.
		

Links

• Jianing Song, Table of n, a(n) for n = 1..7280 (All terms <= 10^8)
• Jianing Song, Nontotients, and their factorizations into two totients

Crossrefs

Cf. A002202, A005277, A301587.

Squares of terms of A281187 are terms of this sequence.

Programs

PARI

isA329872(n) = if(!istotient(n), my(v=divisors(n)); for(i=1, (1+#v)\2, if(istotient(v[i])&&istotient(n/v[i]), return(1))); 0); \\ improved by Jinyuan Wang, Mar 25 2023