A193804 Square array read by antidiagonals: S(n,k) = n - A193805(n,k).
0, 1, 0, 1, 1, 0, 2, 2, 1, 0, 1, 2, 1, 1, 0, 4, 2, 3, 2, 1, 0, 1, 4, 2, 2, 1, 1, 0, 4, 2, 4, 3, 2, 2, 1, 0, 3, 4, 2, 4, 1, 3, 1, 1, 0, 6, 4, 5, 3, 5, 3, 2, 2, 1, 0, 1, 6, 3, 4, 2, 4, 1, 2, 1, 1, 0, 8, 2, 7, 5, 5, 4, 4, 3, 3, 2, 1, 0, 1, 8, 2, 6, 4, 5, 1, 4, 2, 2, 1, 1, 0
Offset: 1
Examples
[x][1][2][3][4][5][6][7][8]
[1] 0, 0, 0, 0, 0, 0, 0, 0
[2] 1, 1, 1, 1, 1, 1, 1, 1
[3] 1, 2, 1, 2, 1, 2, 1, 2
[4] 2, 2, 3, 2, 2, 3, 2, 2
[5] 1, 2, 2, 3, 1, 3, 1, 3
[6] 4, 4, 4, 4, 5, 4, 4, 4
[7] 1, 2, 2, 3, 2, 4, 1, 3
[8] 4, 4, 5, 4, 5, 5, 5, 4
Triangle k=1..n, n>=1:
[1] 0
[2] 1, 1
[3] 1, 2, 1
[4] 2, 2, 3, 2
[5] 1, 2, 2, 3, 1
[6] 4, 4, 4, 4, 5, 4
[7] 1, 2, 2, 3, 2, 4, 1
[8] 4, 4, 5, 4, 5, 5, 5, 4
Triangle n=1..k, k>=1:
[1] 0
[2] 0, 1
[3] 0, 1, 1
[4] 0, 1, 2, 2
[5] 0, 1, 1, 2, 1
[6] 0, 1, 2, 3, 3, 4
[7] 0, 1, 1, 2, 1, 4, 1
[8] 0, 1, 2, 2, 3, 4, 3, 4
S(15, 22) = card({2,3,5,6,9,10,11,12,15}) = 9 as
the defining set is {1,2,..,15} minus {1,4,7,8,13,14}.
Links
- Peter Luschny, Euler's totient function
Programs
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Maple
strongdivisors := n -> numtheory[divisors](n) minus {1}: coprimes := n -> select(k->igcd(k,n)=1,{$1..n}): S := (n,k) -> nops({seq(i,i={$1..n})} minus((coprimes(n) minus strongdivisors(k)))): seq(seq(S(n-k+1,k), k=1..n), n=1..8); # Square array by antidiagonals. seq(print(seq(S(n, k), k=1..n)), n=1..8); # Lower triangle. seq(print(seq(S(n, k), n=1..k)), k=1..8); # Upper triangle. -
Mathematica
s[n_, k_] := Complement[ Range[n], Complement[ Select[ Range[n], CoprimeQ[#, n]&], Divisors[k] // Rest]] // Length; Table[ s[n-k+1, k], {n, 1, 13}, {k, 1, n}] // Flatten (* Jean-François Alcover, Jul 30 2013 *)
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