

A289835


Number of units u in Z/(2n1)Z such that Phi(4,u) is a unit, where Phi is the cyclotomic polynomial.


1



1, 2, 2, 6, 6, 10, 10, 4, 14, 18, 12, 22, 10, 18, 26, 30, 20, 12, 34, 20, 38, 42, 12, 46, 42, 28, 50, 20, 36, 58, 58, 36, 20, 66, 44, 70, 70, 20, 60, 78, 54, 82, 28, 52, 86, 60, 60, 36, 94, 60, 98, 102, 24, 106, 106, 68, 110, 44, 60, 84, 110, 76, 50, 126, 84
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OFFSET

1,2


COMMENTS

If k is even, the number of units u in Z/kZ such that Phi(4,u) is a unit is zero.


LINKS

Jordan Lenchitz, Table of n, a(n) for n = 1..1000


MAPLE

m:=4 do for t from 1 to 1000 do n:=2*t1: S:={}: for a from 0 to n1 do if gcd(a, n)=1 and gcd(cyclotomic(m, a), n)=1 then S:={op(S), a}: fi: od: print(t, nops(S)): od: od:


PROG

(PARI) a(n) = sum(k=0, 2*n2, (gcd(2*n1, k)==1) && (gcd(2*n1, polcyclo(4, k))==1)); \\ Michel Marcus, Jul 29 2017


CROSSREFS

Cf. A058026, A289460.
Sequence in context: A222734 A151888 A320046 * A168276 A039722 A237363
Adjacent sequences: A289832 A289833 A289834 * A289836 A289837 A289838


KEYWORD

nonn,mult,easy


AUTHOR

Jordan Lenchitz, Michael Mueller, Tristan Phillips, Madison Wellen, Eric Jovinelly, Joshua Harrington, Jul 25 2017


STATUS

approved



