A079695 -id:A079695 - cp's OEIS frontend

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

Bernard Schott, Oct 19 2020

nonn

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).

			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.

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

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.

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

a(n) = my(p=2); while (istotient(p*n), p = nextprime(p+1)); p; \\ Michel Marcus, Oct 19 2020

a(A079695(n)) = 2.

A280801 Least k > 0 such that (2*n)^k is in A002202, or 0 if no such k exists.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 4, 1, 3, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 5, 1, 1, 2, 1, 1, 2, 3, 1, 1, 1, 1, 15, 1, 2, 1, 2, 1, 3, 1, 1, 1, 1, 1, 1, 1, 2, 1, 3, 1, 7, 2, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 2, 1, 1, 3, 3, 1, 8, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 4, 1, 2, 2, 1, 1, 4, 1, 1, 1, 17, 1, 2, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 1, 2, 5, 2, 2, 1, 1, 4, 1, 3

Offset: 1

Altug Alkan, Jan 08 2017

nonn

Least k such that A280801(k) = n, or 0 if no such k exists are 1, 7, 19, 17, 31, 223, 61, 79, 151, 383, 181, 347, 523, 1109, 43, 607, 101, 733, 1033, 409, 1783, 1123, 199, 1471, 1301, 5113, 1801, 2311, 3617, 1699, 1543, 7489, 2663, 4583, 7829, 2749, 4177, 5179, 2389, 13291, 20389, ...
What is the asymptotic behavior of this sequence?
Conjecture: a(n) > 0 for all values of n. - Altug Alkan, Jan 11 2017

			a(43) = 15 because (43*2)^k is not in A002202 for 0 < k < 15 and 86^15 = 104106241746467411129608011776 is in A002202.

Giovanni Resta, Table of n, a(n) for n = 1..1000

Cf. A000010, A002180, A002202, A079695.

a(n) = {my(k = 1); while (!istotient((2*n)^k), k++); k; }

a(n) = 1 for n in A002180; a(n) <> 1 for n in A079695. - Michel Marcus, Jan 08 2017

cp's OEIS Frontend

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

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