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 A374001 a(n) is the number of elements z of Z_p[i] such that #{z^k, k >= 0} = p^2-1 (where p denotes A002145(n), the n-th prime number congruent to 3 modulo 4). 1
 4, 16, 32, 96, 160, 256, 480, 704, 896, 1280, 1152, 1536, 1920, 3072, 3744, 4608, 3840, 4224, 5760, 8640, 7872, 8448, 9216, 9600, 9984, 13824, 16128, 12288, 14400, 20800, 18432, 25760, 23040, 23040, 26240, 38528, 34176, 42240, 31104, 48640, 34560, 48384, 46080 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Z_p[i] is a field iff p is a prime number congruent to 3 modulo 4. a(n) is the number of generators of the multiplicative group Z_p[i] \ {0} (where p denotes A002145(n)). LINKS Table of n, a(n) for n=1..43. Rémy Sigrist, Scatterplot of (x, y) such that #{(x+i*y)^k, k >= 0} = p^2-1 (with p = A002145(62) = 647) Rémy Sigrist, C++ program StackExchange, Z_p[i] is a field? EXAMPLE For n = 2: - the second prime number congruent to 3 modulo 4 is p = 7, - the number of elements of {(x + i*y)^k, k >= 0} where x and y belong to Z_7 are: x\y | 0 1 2 3 4 5 6 ----+-------------------------- 0 | 2 4 12 12 12 12 4 1 | 1 24 48 48 48 48 24 2 | 3 48 8 16 16 8 48 3 | 6 48 16 24 24 16 48 4 | 3 48 16 24 24 16 48 5 | 6 48 8 16 16 8 48 6 | 2 24 48 48 48 48 24 - the number 48 appears 16 times, so a(2) = 16. PROG (C++) // See Links section. CROSSREFS Cf. A002145, A271586, A373624. Sequence in context: A126032 A296819 A034713 * A101653 A043100 A329853 Adjacent sequences: A373998 A373999 A374000 * A374002 A374003 A374004 KEYWORD nonn AUTHOR Rémy Sigrist, Jun 24 2024 STATUS approved

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Last modified September 11 08:57 EDT 2024. Contains 375814 sequences. (Running on oeis4.)