OFFSET
1,1
COMMENTS
10 is the smallest totient number that is not in A301587.
If 10*phi(m) is a nontotient, then m is divisible by 121 but not by 5, so every term is divisible by 110.
Proof. In the following cases, 10*phi(m) is a totient number:
(a) If m is not divisible by 11, then phi(11*m) = phi(11)*phi(m) = 10*phi(m).
(b) If m is divisible by 11 but not by 121 or 5, then phi((m/11)*125) = phi(m/11)*phi(125) = (phi(m)/10)*100 = 10*phi(m).
(c) If m is divisible by 5 but not by 2, then phi(4*5*m) = phi(4)*phi(5*m) = 2*(5*phi(m)) = 10*phi(m).
(d) If m is divisible by 5 and 2, then phi(10*m) = 10*phi(m).
So the only left case is that m is divisible by 121 but not by 5.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
110 is a term since 110 = phi(121) = phi(242), but phi(n) = 10*110 = 1100 has no solution.
13310 is a term since 13310 = phi(14641) = phi(29282), but phi(n) = 10*13310 = 133100 has no solution.
PROG
(PARI) isA350320(n) = istotient(n) && !istotient(10*n)
CROSSREFS
KEYWORD
nonn
AUTHOR
Jianing Song, Dec 24 2021
STATUS
approved