A296233 Numbers k such that U(i) is not isomorphic to U(k) for all i < k, where U(k) is the multiplicative group of integers modulo k.

1, 3, 5, 7, 8, 11, 13, 15, 17, 19, 21, 23, 24, 25, 29, 31, 32, 33, 35, 37, 40, 41, 43, 47, 51, 53, 55, 56, 57, 59, 61, 63, 65, 67, 69, 71, 73, 77, 79, 80, 81, 83, 85, 87, 88, 89, 91, 95, 96, 97, 101, 103, 104, 107, 109, 113, 115, 119, 120, 121, 123, 127, 128

Offset: 1

Author

Jianing Song, Apr 29 2018

Keywords

• nonn

Comments

Numbers k such that A289626(i) < A289626(k) for all i < k.

All odd primes are in this sequence. This sequence contains almost all odd numbers.

Numbers k divisible by 2 but not by 4 are not members since U(k) is isomorphic to U(k/2) (i.e., 2, 6, 10, 14, ... are not terms).

Numbers k divisible by 4 but not by 3 or 8 are not members since U(k) is isomorphic to U(3/4*k) (i.e., 4, 20, 28, 44, ... are not terms).

Numbers k divisible by 12 but not by 24 or 36 are not members since U(k) is isomorphic to U(2/3*k) (i.e., 12, 60, 84, 132, ... are not terms).

Numbers k divisible by 9 but not by 7 or 27 are not members since U(k) is isomorphic to U(7/9*k) (i.e., 9, 18, 36, 45, 72, ... are not terms).

Numbers k divisible by 27 but not by 19 or 81 are not members since U(k) is isomorphic to U(19/27*k) (i.e., 27, 54, 108, 135, ... are not terms).

First term == 4 (mod 8) is 252.

Examples

			75 is not a term because U(55) and U(75) are both isomorphic to C_2 x C_20.
93 is not a term because U(77) and U(93) are both isomorphic to C_2 x C_30.
96 is a term because U(96) is isomorphic to C_2 x C_2 x C_8 and U(k) is not isomorphic to C_2 x C_2 x C_8 for all k < 96.
		

Links

• Jianing Song, Table of n, a(n) for n = 1..6527 (All terms <= 16384.)
• Wikipedia, Multiplicative group of integers modulo n

Crossrefs

Cf. A289625, A289626. A319928 is a subsequence.

Programs

PARI

isA296233(n) = !(sum(i=1,n-1,znstar(i)[2]==znstar(n)[2])) \\ Jianing Song, Oct 04 2018

Formula

a(n) = min{k : A289626(k) = n}. - Jianing Song, Jun 30 2018