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A193804 Square array read by antidiagonals: S(n,k) = n - A193805(n,k). 5
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,7

COMMENTS

Let cophi(n) be the cototient function A051953(n). Then cophi(n) = S(n,1) = S(n,n).

LINKS

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

Peter Luschny, Euler's totient function

EXAMPLE

[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}.

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-Fran├žois Alcover, Jul 30 2013 *)

CROSSREFS

Cf. A000010, A051953, A193805.

Sequence in context: A290453 A108423 A208568 * A180424 A092339 A079693

Adjacent sequences:  A193801 A193802 A193803 * A193805 A193806 A193807

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, Aug 06 2011

STATUS

approved

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Last modified June 2 10:43 EDT 2020. Contains 334770 sequences. (Running on oeis4.)