login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A252911 Irregular triangular array read by rows: T(n,k) is the number of elements in the multiplicative group of integers modulo n that have order k, n>=1, 1<=k<=A002322(n). 1
1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 1, 1, 1, 1, 2, 0, 0, 2, 1, 3, 1, 1, 2, 0, 0, 2, 1, 1, 0, 2, 1, 1, 0, 0, 4, 0, 0, 0, 0, 4, 1, 3, 1, 1, 2, 2, 0, 2, 0, 0, 0, 0, 0, 4, 1, 1, 2, 0, 0, 2, 1, 3, 0, 4, 1, 3, 0, 4, 1, 1, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 8, 1, 1, 2, 0, 0, 2, 1, 1, 2, 0, 0, 2, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 6, 1, 3, 0, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,10

COMMENTS

Row sums are A000010.

Column 2 = A155828(n) = A060594(n) - 1.

LINKS

Alois P. Heinz, Rows n = 1..250, flattened

Eric Weisstein's World of Mathematics, Modulo Multiplication Group.

EXAMPLE

1;

1;

1, 1;

1, 1;

1, 1, 0, 2;

1, 1;

1, 1, 2, 0, 0, 2;

1, 3;

1, 1, 2, 0, 0, 2;

1, 1, 0, 2;

1, 1, 0, 0, 4, 0, 0, 0, 0, 4;

1, 3;

1, 1, 2, 2, 0, 2, 0, 0, 0, 0, 0, 4;

1, 1, 2, 0, 0, 2;

1, 3, 0, 4;

T(15,2)=3 because the elements 4, 11, and 14 have order 2 in the modulo multiplication group (Z/15Z)*. We observe that 4^2, 11^2, and 14^2 are congruent to 1 mod 15.

MAPLE

with(numtheory):

T:= n-> `if`(n=1, 1, (p-> seq(coeff(p, x, j), j=1..degree(p)))(

         add(`if`(igcd(n, i)>1, 0, x^order(i, n)), i=1..n-1))):

seq(T(n), n=1..30);  # Alois P. Heinz, Dec 30 2014

MATHEMATICA

Table[Table[

   Count[Table[

     MultiplicativeOrder[a, n], {a,

      Select[Range[n], GCD[#, n] == 1 &]}], k], {k, 1,

    CarmichaelLambda[n]}], {n, 1, 20}] // Grid

CROSSREFS

Cf. A000010, A002322, A054522, A060594, A155828.

Sequence in context: A154243 A326698 A299432 * A176820 A328384 A016024

Adjacent sequences:  A252908 A252909 A252910 * A252912 A252913 A252914

KEYWORD

nonn,tabf

AUTHOR

Geoffrey Critzer, Dec 24 2014

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 19 21:47 EST 2020. Contains 331066 sequences. (Running on oeis4.)