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%I #148 Aug 11 2023 09:51:54
%S 0,0,30,0,10,0,2,0,10,110,22,0,2,22,6,0,2,0,2,0,54,22,10,0,2,22,22,
%T 212983792,6
%N Least totient number k > 1 such that n*k is a nontotient number, or 0 if no such number exists.
%C After a(30) which is unknown, the sequence continues: 2, 0, 18, 2, 10, 0, 2, 2, 6, 0, 6, 0, 2, 22, 2, 46, 2, 0, 2, 22, 10, 146068, 6, 0, 10, and a(56) is unknown. - _Michel Marcus_, Mar 11 2023
%C When n is in A002202, then n*a(n) is a term of A329872; in other words a(n) is the value k, such that k*a(n) is the least term of A329872 that is divisible by n. - _Michel Marcus_, Mar 26 2023
%C a(30) > 2.5*10^10, if it is not 0. - _Amiram Eldar_, May 07 2023
%C a(568) <= 2^17*71^13 where 568 = 2^3*71 (so similar to a(652) = 2^4*163^3 where 652 = 2^2*163). - _Michel Marcus_, May 14 2023
%C From _Michel Marcus_, Jun 08 2023: (Start)
%C Experimentally there are 2 cases: n is a totient value or is a nontotient.
%C If n is a nontotient, then it is relatively easy to find the titular k.
%C If n is a totient value, then we see that there are 4 cases:
%C there are no such k and a(n)=0,
%C k is known, and by definition k is a totient value.
%C k is not known but we know a large totient value K for which n*K is nontotient,
%C k is currently unknown.
%C For several k or K, n*k are squares of terms of A281187. (End)
%H Math Overflow, <a href="https://mathoverflow.net/questions/307392/the-range-of-the-euler-totient-function-and-multiplication-by-28">The range of the Euler totient function and multiplication by 28</a>, 2018.
%H Michel Marcus, <a href="/A361058/a361058_2.txt">Known results</a>, Aug 11 2023.
%F a(n) = 0 if n is in A301587.
%F a(A007617(n)) = A350085(n). - _Michel Marcus_, Apr 08 2023
%e a(3) = 30 because 30 is in A002202 and 3*30 = 90 is in A007617.
%o (PARI) a(n) = if (vecsearch([1, 2, 4, 6, 8, 12, 16, 18, 20, 24], n), return(0)); my(k=2); while (istotient(n*k), k++; while (!istotient(k), k++)); k; \\ _Michel Marcus_, Mar 08 2023
%o (PARI) check(n, k) = istotient(k) && !istotient(n*k); \\ _Michel Marcus_, Apr 05 2023; just for checking
%Y Cf. A002202 (totient numbers), A007617 (nontotient numbers).
%Y Cf. A281187, A301587, A316665, A329872, A350085, A350086.
%K nonn,more
%O 1,3
%A _Jinyuan Wang_, Mar 01 2023
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