A117974 Triangle where a(1,1)=1; a(n,m) = number of positive integers which are missing from row (n-1) of the triangle, are <= m and are coprime to m.

1, 0, 0, 1, 1, 2, 0, 0, 0, 1, 0, 0, 1, 1, 3, 0, 0, 1, 0, 2, 1, 0, 0, 0, 1, 2, 1, 4, 0, 0, 0, 1, 1, 1, 3, 3, 0, 0, 1, 0, 2, 1, 4, 2, 5, 0, 0, 0, 1, 1, 0, 2, 2, 2, 3, 0, 0, 0, 0, 1, 1, 3, 2, 4, 2, 7, 0, 0, 0, 0, 0, 1, 2, 1, 2, 1, 5, 2, 0, 0, 0, 1, 2, 0, 3, 2, 3, 3, 7, 2, 9, 0, 0, 0, 0, 1, 1, 3, 1, 3, 0, 5, 2, 7, 3

Offset

1,6

Links

Table of n, a(n) for n=1..105.

Example

Row 5 of the triangle is [0,0,1,1,3]. There are 0 positive integers which are coprime to 1, are <= 1 and are not among the terms of row 5 (because 1 occurs in row 5). There are 0 positive integers which are <= 2, are coprime to 2 and are not among the terms of row 5. ...(Skipping over the m = 3, 4 and 5 cases.) There is 1 positive integer (5) which is <= 6, is coprime to 6 and does not occur in row 5.
So row 6 is [0,0,1,0,2,1].

Maple

A117974 := proc(nrow) local a, aprev, anm, m, k ; if nrow = 1 then [1] ; else a := [] ; aprev := A117974(nrow-1) ; for m from 1 to nrow do anm := 0 ; for k from 1 to m do if not k in aprev and gcd(k, m) = 1 then anm := anm+1 ; fi ; od: a := [op(a), anm] ; od; RETURN(a) ; fi ; end: seq(op(A117974(n)), n=1..20) ; # R. J. Mathar, Sep 05 2007

Crossrefs

Cf. A117975.

Sequence in context: A243224 A127324 A083917 * A369927 A328037 A193426

Adjacent sequences: A117971 A117972 A117973 * A117975 A117976 A117977

Keyword

nonn,tabl

Author

Leroy Quet, Apr 06 2006

Extensions

More terms from R. J. Mathar, Sep 05 2007

Status

approved