login
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.
4
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
1,2
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.
LINKS
Jianing Song, Table of n, a(n) for n = 1..6527 (All terms <= 16384.)
FORMULA
a(n) = min{k : A289626(k) = n}. - Jianing Song, Jun 30 2018
EXAMPLE
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.
PROG
(PARI) isA296233(n) = !(sum(i=1, n-1, znstar(i)[2]==znstar(n)[2])) \\ Jianing Song, Oct 04 2018
CROSSREFS
Cf. A289625, A289626. A319928 is a subsequence.
Sequence in context: A168162 A047485 A024969 * A371185 A276112 A228075
KEYWORD
nonn
AUTHOR
Jianing Song, Apr 29 2018
STATUS
approved