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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A198067 Square array read by antidiagonals, n>=1, k>=1; T(n,k) is the number of nonprime numbers which are prime to n and are not strong divisors of k. 2
 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 3, 1, 3, 1, 2, 1, 1, 1, 1, 2, 3, 1, 2, 1, 2, 1, 1, 1, 1, 6, 2, 3, 1, 3, 1, 2, 1, 1, 1, 1, 1, 6, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 7, 1, 6, 2, 3, 1, 3, 1, 2 (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 alpha(n) be number of nonprime numbers in the reduced residue system of n. Then alpha(n) = T(n,1) = T(n,n). LINKS Peter Luschny, Euler's totient function EXAMPLE T(15, 22) = card({1,4,8,14}) = 4 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] 1, 1, 1, 1, 1, 1, 1, 1 [2] 1, 1, 1, 1, 1, 1, 1, 1 [3] 1, 1, 1, 1, 1, 1, 1, 1 [4] 1, 1, 1, 1, 1, 1, 1, 1 [5] 2, 2, 2, 1, 2, 2, 2, 1 [6] 1, 1, 1, 1, 1, 1, 1, 1 [7] 3, 3, 3, 2, 3, 2, 3, 2 [8] 1, 1, 1, 1, 1, 1, 1, 1 - Triangle k=1..n, n>=1: [1]           1 [2]          1, 1 [3]        1, 1, 1 [4]       1, 1, 1, 1 [5]     2, 2, 2, 1, 2 [6]    1, 1, 1, 1, 1, 1 [7]  3, 3, 3, 2, 3, 2, 3 [8] 1, 1, 1, 1, 1, 1, 1, 1 - Triangle n=1..k, k>=1: [1]           1 [2]          1, 1 [3]        1, 1, 1 [4]       1, 1, 1, 1 [5]     1, 1, 1, 1, 2 [6]    1, 1, 1, 1, 2, 1 [7]  1, 1, 1, 1, 2, 1, 3 [8] 1, 1, 1, 1, 1, 1, 2, 1 MAPLE strongdivisors := n -> numtheory[divisors](n) minus {1}: coprimes  := n -> select(k->igcd(k, n)=1, {\$1..n}): nonprimes := n -> remove(isprime, {\$1..n}); T := (n, k) -> nops(nonprimes(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. CROSSREFS Cf. A000010, A048864, A193804, A193805, A198066. Sequence in context: A211111 A074971 A344008 * A282749 A132587 A318930 Adjacent sequences:  A198064 A198065 A198066 * A198068 A198069 A198070 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.

Last modified September 21 07:28 EDT 2021. Contains 347596 sequences. (Running on oeis4.)