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

1,1

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.

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

Example

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.

Prog

(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

Crossrefs

Cf. A002202, A005277, A301587.

Squares of terms of A281187 are terms of this sequence.

Sequence in context: A156646 A177434 A202444 * A199330 A281398 A014803

Adjacent sequences: A329869 A329870 A329871 * A329873 A329874 A329875

Keyword

nonn

Author

Jianing Song, Nov 23 2019

Status

approved