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a(1)=1. a(n) = a(n-1) + (number of earlier terms {i.e., terms a(1) through a(n-1)} that divide n).
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%I #16 Jan 26 2019 03:14:16

%S 1,2,3,5,7,10,12,14,16,20,21,25,26,30,33,36,37,40,41,46,50,52,53,57,

%T 60,63,65,69,70,76,77,80,83,85,88,93,95,97,99,105,107,113,114,116,119,

%U 122,123,128,130,136,138,142,144,147,149,153,156,158,159,168,169,171,176

%N a(1)=1. a(n) = a(n-1) + (number of earlier terms {i.e., terms a(1) through a(n-1)} that divide n).

%e Among terms a(1) through a(5) there are three terms that divide 6: a(1)=1, a(2)=2 and a(3)=3. So a(6) = a(5) + 3 = 10.

%p A123885 := proc(maxn) local a,nexta,n,i; a := [1]; for n from 2 to maxn do nexta := op(n-1,a); for i from 1 to n-1 do if n mod op(i,a) = 0 then nexta := nexta +1; fi; od; a := [op(a), nexta]; od; RETURN(a); end: maxn := 100 : alist := A123885(maxn) : for i from 1 to maxn do printf("%d,",op(i,alist)); end : # _R. J. Mathar_, Oct 21 2006

%t f[l_List] := Append[l, Last[l] + Length[Select[l, Mod[Length[l] + 1, # ] == 0 &]]];Nest[f, {1}, 63] (* _Ray Chandler_, Oct 19 2006 *)

%Y Cf. A123886.

%K easy,nonn

%O 1,2

%A _Leroy Quet_, Oct 17 2006

%E Extended by _Ray Chandler_, Oct 19 2006

%E More terms from _R. J. Mathar_, Oct 21 2006