A117974 - OEIS

%I #11 Aug 09 2015 15:36:26

%S 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,

%T 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,

%U 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

%N 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.

%e 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.

%e So row 6 is [0,0,1,0,2,1].

%p 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

%Y Cf. A117975.

%K nonn,tabl

%O 1,6

%A _Leroy Quet_, Apr 06 2006

%E More terms from _R. J. Mathar_, Sep 05 2007