A372755 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.

252, 324, 2052, 2268, 3276, 4788, 6156, 7452, 7812, 10836, 12348, 14364, 14868, 15228, 16884, 17172, 18396, 19908, 20916, 22572, 23652, 24444, 25596, 25956, 26244, 26892, 26964, 31428, 34668, 35028, 35316, 38052, 38988, 41076, 43092, 43596, 45108, 48636, 48924, 52812, 56052, 56196, 57204

Offset: 1

Author

Jianing Song, May 12 2024

Keywords

• nonn

Comments

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.

Examples

			252 is a term because there is no other k such that (Z/kZ)* = (Z/252Z)* = C_2 X C_6 X C_6.
324 is a term because there is no other k such that (Z/kZ)* = (Z/324Z)* = C_2 X C_54.
2052 is a term because there is no other k such that (Z/kZ)* = (Z/2052Z)* = C_2 X C_18 X C_18.
		

Links

• Jianing Song, Table of n, a(n) for n = 1..145
• Wikipedia, Multiplicative group of integers modulo n

Crossrefs

Cf. A296233, A319928.

Programs

PARI

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