%I #37 Jul 01 2021 01:42:21

%S 7,1,10,2,28,56,4,6,460,232,64,300,328,12,256,180,176,84,36,132,1400,

%T 984,2200,780,1332,280,1664,1672,72,8136,420,53244,1960,60,2320,5928,

%U 264,936,24,32604,6696,2976,2268,6372,312,1380,48,320,2560,816,16500,4860

%N a(n) is the least m such that A338266(m) = prime(n), where A338266(m) is the least prime p such that p*m is not a totient number.

%C Zhang Ming-Zhi has shown that for every positive integer m, there is a prime p such that m*p is not a totient (see Reference, link: theorem 1). A338266 gives the smallest prime p that is such linked to m.

%D Richard K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004, Section B36, p. 139.

%H Zhang Ming-Zhi, <a href="https://doi.org/10.1006/jnth.1993.1014">On Nontotients</a>, J. Number Theory, Vol. 43, No. 2 (1993), pp. 168-172.

%e Prime(2)=3 is the smallest prime such that 3*1=3, 3*3=9, 3*9=27, 3*11=33, 3*15=45,... are not totient (A338266), and 1 is the smallest number of the set {1, 3, 9, 11, 15...} linked to prime(2), so a(2)=1.

%o (PARI) f(n) = my(p=2); while (istotient(p*n), p = nextprime(p+1)); p; \\ A338266

%o a(n) = my(k=1, p=prime(n)); while(f(k) != p, k++); k; \\ _Michel Marcus_, Nov 03 2020

%Y Cf. A000010, A002202, A007617, A071615, A338266.

%K nonn

%O 1,1

%A _Bernard Schott_, Nov 02 2020

%E More terms from _Amiram Eldar_, Nov 02 2020

%E Name improved by _Amiram Eldar_ and _Michel Marcus_, Nov 03 2020