

A280338


Number of sizes of remainder sets for n, for any natural number c, given natural number b in (b^c) mod n.


1



1, 1, 2, 2, 3, 2, 4, 3, 4, 3, 4, 3, 6, 4, 3, 3, 5, 4, 6, 5, 4, 4, 4, 4, 6, 6, 6, 6, 6, 3, 8, 6, 4, 5, 6, 6, 9, 6, 6, 6, 8, 4, 8, 7, 7, 4, 4, 5, 8, 6, 5, 9, 6, 6, 6, 8, 6, 6, 4, 5, 12, 8, 6, 7, 6, 4, 8, 9, 4, 6, 8, 8, 12, 9, 7, 10, 8, 6, 8, 6, 9, 8, 4, 6, 5, 8
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OFFSET

1,3


LINKS

Jeptha Davenport, Table of n, a(n) for n = 1..500


EXAMPLE

For a(1): b^c mod 1 = 0, so only 1 remainder set (0) is possible, and its size is 1.
For a(2): for any b, b^c will be even if b is even, or odd if b is odd, so b^c mod 2 has only 1 remainder for a given b (either (0), size 1, or (1), also size 1).
For a(5): choosing c for an arbitrary b, for b = 2, 2^2 mod 5 = 4, 2^3 mod 5 = 3, 2^4 mod 5 = 1, 2^5 mod 5 = 2, 2^6 mod 5 = 4, etc. (4 remainders); for base 4, 4^1 mod 5 = 4, 4^2 mod 5 = 1, 4^3 mod 5 = 4, etc. (2 remainders); for base 21, 21^1 mod 5 = 1, 21^819 mod 5 = 1, etc. (1 remainder); these are the only numbers of remainders which occur for any c given b for b^c modulo 5, so the number of remainder set sizes for n = 5 is 3 (4, 2, or 1size remainder sets).
For a(100): number of remainder set sizes possible for any c given b is 10 (1, 2, 3, 4, 5, 6, 10, 11, 20, or 21size remainder sets).


CROSSREFS

First differs from A062821 at index n=15.
Sequence in context: A106737 A323164 A318881 * A062821 A296080 A180633
Adjacent sequences: A280335 A280336 A280337 * A280339 A280340 A280341


KEYWORD

nonn


AUTHOR

Jeptha Davenport, Dec 31 2016


STATUS

approved



