cp's OEIS Frontend

A350320 Totient numbers k such that 10*k is a nontotient.

%I A350320 #15 Jul 19 2024 08:47:26
%S A350320 110,13310,18260,78980,130460,143660,163460,164780,167420,284900,
%T A350320 325160,329780,332420,370700,381260,403700,418220,431420,453860,
%U A350320 514580,526460,535700,554180,560780,603020,628100,646580,665060,675620,732380,745580,765380,801020
%N A350320 Totient numbers k such that 10*k is a nontotient.
%C A350320 10 is the smallest totient number that is not in A301587.
%C A350320 If 10*phi(m) is a nontotient, then m is divisible by 121 but not by 5, so every term is divisible by 110.
%C A350320 Proof. In the following cases, 10*phi(m) is a totient number:
%C A350320 (a) If m is not divisible by 11, then phi(11*m) = phi(11)*phi(m) = 10*phi(m).
%C A350320 (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 A350320 (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).
%C A350320 (d) If m is divisible by 5 and 2, then phi(10*m) = 10*phi(m).
%C A350320 So the only left case is that m is divisible by 121 but not by 5.
%H A350320 Amiram Eldar, <a href="/A350320/b350320.txt">Table of n, a(n) for n = 1..10000</a>
%e A350320 110 is a term since 110 = phi(121) = phi(242), but phi(n) = 10*110 = 1100 has no solution.
%e A350320 13310 is a term since 13310 = phi(14641) = phi(29282), but phi(n) = 10*13310 = 133100 has no solution.
%o A350320 (PARI) isA350320(n) = istotient(n) && !istotient(10*n)
%Y A350320 Totient numbers k such that m*k is a nontotient: A350316 (m=3), A350317 (m=5), A350318 (m=7), A350319 (m=9), this sequence (m=10), A350321 (m=14).
%Y A350320 Cf. A002202, A005277, A301587.
%K A350320 nonn
%O A350320 1,1
%A A350320 _Jianing Song_, Dec 24 2021