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A338266 Least prime p such that p*n is not a totient number. 2
3, 7, 3, 17, 3, 19, 2, 19, 3, 5, 3, 43, 2, 7, 3, 19, 2, 5, 2, 17, 3, 7, 3, 167, 2, 7, 3, 11, 3, 3, 2, 19, 3, 2, 3, 67, 2, 2, 3, 17, 3, 17, 2, 7, 2, 5, 2, 211, 2, 7, 3, 7, 3, 11, 3, 13, 2, 3, 2, 139, 2, 2, 3, 31, 3, 19, 2, 5, 3, 5, 2, 109, 2, 5, 3, 2, 2, 3, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Zhang Ming-Zhi has shown that for every positive integer n, there is a prime p such that p*n is not a totient (see Reference and link, theorem 1).
Differs from A282160, where multiplier p is not requested to be prime, for n = 6, 66, 80, 126, ... those indices where A282160(n) is not prime (see Example).
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.
FORMULA
a(A079695(n)) = 2.
EXAMPLE
a(6) = 19 because 19 * 6 = 114 is not a totient number and 19 is the least prime with this property. Also 15 * 6 = 90 is not either a totient number, so A282160(6) = 15 that is not a prime number.
PROG
(PARI) a(n) = my(p=2); while (istotient(p*n), p = nextprime(p+1)); p; \\ Michel Marcus, Oct 19 2020
CROSSREFS
Sequence in context: A201385 A186107 A282160 * A019158 A367865 A086153
KEYWORD
nonn
AUTHOR
Bernard Schott, Oct 19 2020
STATUS
approved

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Last modified March 29 06:57 EDT 2024. Contains 371265 sequences. (Running on oeis4.)