%I A054519
%S A054519 1,2,4,6,9,11,15,17,21,24,28,30,36,38,42,46,51,53,59,61,67,71,75,77,85,
%T A054519 88,92,96,102,104,112,114,120,124,128,132,141,143,147,151,159,161,169,
%U A054519 171,177,183
%N A054519 Number of increasing arithmetic progressions ending in n (in the nonnegative 
               integers), including those of length 1 or 2.
%C A054519 a(0)=1, a(n)=a(n-1) + sigma_0(n), in terms of OEIS a(n)=a(n-1)+A000005(n). 
               [From Ctibor O. Zizka (c.zizka(AT)email.cz), Nov 08 2008]
%H A054519 T. D. Noe, <a href="b054519.txt">Table of n, a(n) for n=0..1000</a>
%F A054519 a(n) = A051336(n+1)-A051336(n) = a(n-1)+A000005(n) = A006218(n)+1.
%e A054519 a(3)=6 because the six increasing progressions (3), (2,3), (1,2,3), (0,
               1,2,3), (1,3) and (0,3) all end in 3.
%p A054519 IBI:= {{}}: a[0]:= 1: for n from 1 to 45 do IBI:= IBI union map(t -> 
               t union {n}, select(t -> (t minus map(q -> n-q, t)={}), IBI)); a[n]:= 
               nops(IBI) od: seq(a[n], n=0..45); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Mar 18 2007
%p A054519 with(numtheory):a[1]:=2: for n from 2 to 59 do a[n]:=a[n-1]+tau(n) od: 
               seq(a[n], n=0..45);# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Mar 21 2009]
%Y A054519 Cf. A000005, A006218, A051336. Left edge of A056535.
%Y A054519 Sequence in context: A050502 A022760 A164286 this_sequence A038107 A153196 
               A077220
%Y A054519 Adjacent sequences: A054516 A054517 A054518 this_sequence A054520 A054521 
               A054522
%K A054519 easy,nonn,nice
%O A054519 0,2
%A A054519 Henry Bottomley (se16(AT)btinternet.com), Apr 07 2000