login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A198066 Square array read by antidiagonals, n>=1, k>=1; T(n,k) is the number of primes which are prime to n and are not strong divisors of k. 2
0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 3, 1, 1, 1, 1, 0, 0, 3, 2, 1, 1, 1, 0, 0, 0, 3, 3, 2, 1, 2, 0, 1, 0, 0, 2, 2, 2, 2, 0, 0, 1, 0, 0, 0, 4, 2, 3, 3, 2, 1, 2, 1, 1, 0, 0, 3, 3, 1, 2, 2, 1, 1, 1, 0, 0, 0, 0, 5, 3, 3, 2, 2, 2, 3, 1, 1, 1, 1, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,11

COMMENTS

We say d is a strong divisor of n iff d is a divisor of n and d > 1. Let prime_phi(n) be number of primes in the reduced residue system mod n. Then prime_phi(n) = T(n,1) = T(n,n).

LINKS

Table of n, a(n) for n=1..91.

Peter Luschny, Euler's totient function

EXAMPLE

T(15, 22) = card({7,13}) = 2 because the coprimes of 15 are {1,2,4,7,8,11,13,14} and the strong divisors of 22 are {2,11,22}.

-

[x][1][2][3][4][5][6][7][8]

[1] 0, 0, 0, 0, 0, 0, 0, 0

[2] 0, 0, 0, 0, 0, 0, 0, 0

[3] 1, 0, 1, 0, 1, 0, 1, 0

[4] 1, 1, 0, 1, 1, 0, 1, 1

[5] 2, 1, 1, 1, 2, 0, 2, 1

[6] 1, 1, 1, 1, 0, 1, 1, 1

[7] 3, 2, 2, 2, 2, 1, 3, 2

[8] 3, 3, 2, 3, 2, 2, 2, 3

-

Triangle k=1..n, n>=1:

[1]           0

[2]          0, 0

[3]        1, 0, 1

[4]       1, 1, 0, 1

[5]     2, 1, 1, 1, 2

[6]    1, 1, 1, 1, 0, 1

[7]  3, 2, 2, 2, 2, 1, 3

[8] 3, 3, 2, 3, 2, 2, 2, 3

-

Triangle n=1..k, k>=1:

[1]            0

[2]           0, 0

[3]         0, 0, 1

[4]        0, 0, 0, 1

[5]      0, 0, 1, 1, 2

[6]     0, 0, 0, 0, 0, 1

[7]   0, 0, 1, 1, 2, 1, 3

[8]  0, 0, 0, 1, 1, 1, 2, 3

MAPLE

strongdivisors := n -> numtheory[divisors](n) minus {1}:

coprimes := n -> select(k->igcd(k, n)=1, {$1..n}):

primes := n -> select(isprime, {$1..n}):

T := (n, k) -> nops(primes(n) intersect (coprimes(n) minus strongdivisors(k))):

seq(seq(T(n-k+1, k), k=1..n), n=1..13);  # Square array by antidiagonals.

seq(print(seq(T(n, k), k=1..n)), n=1..8); # Lower triangle.

seq(print(seq(T(n, k), n=1..k)), k=1..8); # Upper triangle.

MATHEMATICA

T[n_, k_] := Complement[Select[Range[n-1], PrimeQ[#] && CoprimeQ[#, n]&], Rest[Divisors[k]]] // Length;

Table[T[n-k+1, k], {n, 1, 13}, {k, 1, n}] (* Jean-Fran├žois Alcover, Jun 29 2019 *)

CROSSREFS

Cf. A000010, A048865, A193804, A193805, A198067.

Sequence in context: A004610 A068934 A035200 * A141664 A056979 A087812

Adjacent sequences:  A198063 A198064 A198065 * A198067 A198068 A198069

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, Nov 07 2011

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 November 20 14:54 EST 2019. Contains 329337 sequences. (Running on oeis4.)