A372755 - OEIS

%I #16 May 13 2024 00:06:15

%S 252,324,2052,2268,3276,4788,6156,7452,7812,10836,12348,14364,14868,

%T 15228,16884,17172,18396,19908,20916,22572,23652,24444,25596,25956,

%U 26244,26892,26964,31428,34668,35028,35316,38052,38988,41076,43092,43596,45108,48636,48924,52812,56052,56196,57204

%N Terms of A319928 that are congruent to 4 modulo 8: Numbers k == 4 (mod 8) such that there is no other m such that (Z/mZ)* is isomorphic to (Z/kZ)*, where (Z/kZ)* is the multiplicative group of integers modulo k.

%C This is a subsequence of A296233. As a result, all members in this sequence should not satisfy any congruence mentioned there, so terms of A319928 that are congruent to 4 modulo 8 are rare. In particular, all terms are divisible by 252 = 4 * 3^2 * 7, 324 = 4 * 3^4 or 2052 = 4 * 3^3 * 19.

%H Jianing Song, <a href="/A372755/b372755.txt">Table of n, a(n) for n = 1..145</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Multiplicative_group_of_integers_modulo_n">Multiplicative group of integers modulo n</a>

%e 252 is a term because there is no other k such that (Z/kZ)* = (Z/252Z)* = C_2 X C_6 X C_6.

%e 324 is a term because there is no other k such that (Z/kZ)* = (Z/324Z)* = C_2 X C_54.

%e 2052 is a term because there is no other k such that (Z/kZ)* = (Z/2052Z)* = C_2 X C_18 X C_18.

%o (PARI) isA372755(n) = (n % 8 == 4) && isA319928(n)

%Y Cf. A296233, A319928.

%K nonn

%O 1,1

%A _Jianing Song_, May 12 2024