A338266 Least prime p such that p*n is not a totient number.

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

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

Amiram Eldar, Table of n, a(n) for n = 1..10000

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

Cf. A000010, A002202, A061026, A071615, A079695, A282160.

Sequence in context: A201385 A186107 A282160 * A019158 A367865 A086153

Adjacent sequences: A338263 A338264 A338265 * A338267 A338268 A338269

Keyword

nonn

Author

Bernard Schott, Oct 19 2020

Status

approved