A289835 - OEIS

A289835

Number of units u in Z/(2n-1)Z such that Phi(4,u) is a unit, where Phi is the cyclotomic polynomial.

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*t-1: S:={}: for a from 0 to n-1 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*n-2, (gcd(2*n-1, k)==1) && (gcd(2*n-1, 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