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A361686 a(n) is the least totient divisor of A329872(n), where A329872 are nontotients (A005277) that are the product of two totients (A002202).

%I A361686 #11 Mar 29 2023 12:12:04
%S A361686 22,22,10,46,58,46,78,82,58,46,102,22,106,82,46,138,106,82,166,172,
%T A361686 178,190,106,226,82,166,238,172,178,22,106,262,190,282,22,106,310,316,
%U A361686 226,82,166,238,172,346,46,178,22,358,22,10,366,106,262,382,82,388,58,22,22,46,418
%N A361686 a(n) is the least totient divisor of A329872(n), where A329872 are nontotients (A005277) that are the product of two totients (A002202).
%C A361686 Let k be the least instance a(k) = m, then A329872(k) = m*A361058(m). For instance a(3)=10, and A329872(3) = 1100 = 10*110 = 10*A361058(10).
%C A361686 Can we get a(k)=30 or a(k)=52 (see A361058)?
%H A361686 Michel Marcus, <a href="/A361686/b361686.txt">Table of n, a(n) for n = 1..7280</a>
%e A361686 a(3)=10 because A329872(3)=1100 which can be expressed as 1*1100, 2*550, 4*275, 5*220, 10*110, ... where 10*110 is the first case where both factors are nontotients.
%o A361686 (PARI) is(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); \\ A329872
%o A361686 lista(nn) = for (n=1, nn, if (is(n), my(d=divisors(n)); for (i=1, (1+#d)\2, if (istotient(d[i]) && istotient(n/d[i]), print1(d[i], ", "); break););););
%Y A361686 Cf. A002202, A005277, A329872, A361058.
%K A361686 nonn
%O A361686 1,1
%A A361686 _Michel Marcus_, Mar 29 2023