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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.
1
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
1,1
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.
EXAMPLE
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.
PROG
(PARI) isA372755(n) = (n % 8 == 4) && isA319928(n)
CROSSREFS
Sequence in context: A330616 A046331 A066695 * A104396 A207373 A072443
KEYWORD
nonn
AUTHOR
Jianing Song, May 12 2024
STATUS
approved