The On-Line Encyclopedia of Integer Sequences (OEIS)

Revisions by Jordan Lenchitz (See also Jordan Lenchitz's wiki page)

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A290309

Number of units u in Z/nZ such that Phi(5,u) is a unit, where Phi is the cyclotomic polynomial.
(history; published version)

#11 by Jordan Lenchitz at Sat Jul 29 21:58:11 EDT 2017

STATUS

editing

proposed

A290322

Sum modulo n of all units u in Z/nZ such that Phi(5,u) is a unit, where Phi is the cyclotomic polynomial.
(history; published version)

#3 by Jordan Lenchitz at Thu Jul 27 10:47:28 EDT 2017

STATUS

editing

proposed

#2 by Jordan Lenchitz at Thu Jul 27 10:45:49 EDT 2017

NAME

allocated for Jordan LenchitzSum modulo n of all units u in Z/nZ such that Phi(5,u) is a unit, where Phi is the cyclotomic polynomial.

DATA

1, 0, 0, 4, 0, 0, 0, 0, 9, 1, 0, 0, 0, 3, 0, 0, 0, 0, 8, 0, 12, 0, 0, 20, 0, 0, 0, 0, 18, 1, 0, 24, 0, 14, 0, 0, 0, 0, 16, 1, 0, 0, 24, 9, 0, 0, 0, 0, 45, 0, 0, 0, 0, 14, 0, 0, 0, 0, 36, 1, 32, 0, 0, 13, 24, 0, 0, 0, 14, 1, 0, 0, 0, 15, 0, 28, 0, 0, 32, 0, 42, 0

OFFSET

2,4

MAPLE

with(numtheory): m:=5: for n from 2 to 100 do S:={}: for a from 1 to n-1 do if gcd(a, n)=1 and gcd(cyclotomic(m, a), n)=1 then S:={op(S), a}: fi: od: print(sum(op(i, S), i=1..nops(S)) mod n): od:

CROSSREFS

Cf. A289460, A058026.

KEYWORD

allocated

nonn

AUTHOR

Joshua Harrington, Michael Mueller, Jordan Lenchitz, Tristan Phillips, Madison Wellen, Eric Jovinelly, Jul 27 2017

STATUS

approved

editing

#1 by Jordan Lenchitz at Thu Jul 27 10:45:49 EDT 2017

NAME

allocated for Jordan Lenchitz

KEYWORD

allocated

STATUS

approved

A290321

Sum modulo n of all units u in Z/nZ such that Phi(3,u) is a unit, where Phi is the cyclotomic polynomial.
(history; published version)

#3 by Jordan Lenchitz at Thu Jul 27 10:31:03 EDT 2017

STATUS

editing

proposed

#2 by Jordan Lenchitz at Thu Jul 27 10:27:10 EDT 2017

NAME

allocated for Jordan LenchitzSum modulo n of all units u in Z/nZ such that Phi(3,u) is a unit, where Phi is the cyclotomic polynomial.

DATA

1, 2, 0, 0, 5, 1, 0, 6, 0, 0, 4, 1, 8, 5, 0, 0, 15, 1, 0, 8, 0, 0, 8, 0, 14, 18, 16, 0, 20, 1, 0, 11, 0, 25, 12, 1, 20, 14, 0, 0, 8, 1, 0, 15, 0, 0, 16, 7, 0, 17, 28, 0, 45, 0, 32, 20, 0, 0, 40, 1, 32, 24, 0, 30, 44, 1, 0, 23, 60, 0, 24, 1, 38, 25, 40, 66, 14, 1

OFFSET

2,2

MAPLE

with(numtheory): m:=3: for n from 2 to 100 do S:={}: for a from 1 to n-1 do if gcd(a, n)=1 and gcd(cyclotomic(m, a), n)=1 then S:={op(S), a}: fi: od: print(sum(op(i, S), i=1..nops(S)) mod n): od:

CROSSREFS

Cf. A289460, A058026.

KEYWORD

allocated

nonn

AUTHOR

Michael Mueller, Jordan Lenchitz, Tristan Phillips, Madison Wellen, Eric Jovinelly, Joshua Harrington, Jul 27 2017

STATUS

approved

editing

#1 by Jordan Lenchitz at Thu Jul 27 10:27:10 EDT 2017

NAME

allocated for Jordan Lenchitz

KEYWORD

allocated

STATUS

approved

A290309

Number of units u in Z/nZ such that Phi(5,u) is a unit, where Phi is the cyclotomic polynomial.
(history; published version)

#5 by Jordan Lenchitz at Thu Jul 27 05:52:12 EDT 2017

STATUS

editing

proposed

#4 by Jordan Lenchitz at Thu Jul 27 05:51:39 EDT 2017

MAPLE

m:=5; T:=[]: for n from 1 to 100 do 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: T:=[op(T), nops(S)]: od: print(m, T):

#3 by Jordan Lenchitz at Thu Jul 27 05:50:24 EDT 2017

COMMENTS

The number of units u in Z/nZ such that Phi(1,u) or Phi(2,u) is a unit is given by A058026. The number of units u in Z/nZ such that Phi(3,u) is a unit is given by A289460.

The number of units u in Z/nZ such that Phi(3,u) is a unit is given by A289460.