OFFSET
1,1
COMMENTS
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.
REFERENCES
Richard K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004, Section B36, p. 139.
LINKS
Zhang Ming-Zhi, On Nontotients, J. Number Theory, Vol. 43, No. 2 (1993), pp. 168-172.
EXAMPLE
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.
PROG
(PARI) f(n) = my(p=2); while (istotient(p*n), p = nextprime(p+1)); p; \\ A338266
a(n) = my(k=1, p=prime(n)); while(f(k) != p, k++); k; \\ Michel Marcus, Nov 03 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Bernard Schott, Nov 02 2020
EXTENSIONS
More terms from Amiram Eldar, Nov 02 2020
Name improved by Amiram Eldar and Michel Marcus, Nov 03 2020
STATUS
approved