A123886 a(0)=1. a(n) = a(n-1) + (number of earlier terms {i.e., terms a(0) through a(n-1)} that divide n).

1, 2, 4, 5, 8, 10, 12, 13, 17, 18, 22, 23, 27, 29, 31, 33, 37, 39, 42, 43, 48, 49, 52, 54, 59, 61, 64, 66, 69, 71, 75, 77, 81, 83, 86, 88, 93, 95, 97, 100, 106, 107, 110, 112, 116, 118, 121, 122, 128, 130, 134, 136, 141, 142, 147, 149, 153, 154, 157, 159, 165, 167, 170

Offset

0,2

Links

A.H.M. Smeets, Table of n, a(n) for n = 0..20000

Example

Among terms a(0) through a(5) there are two terms that divide 6: a(0)=1, a(1)=2. So a(6) = a(5) + 2 = 12.

Maple

A123886 := 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-1) mod op(i, a) = 0 then nexta := nexta +1 ; fi ; od ; a := [op(a), nexta] ; od ; RETURN(a) ; end: maxn := 100 : alist := A123886(maxn) : for i from 1 to maxn do printf("%d, ", op(i, alist)) ; end : # R. J. Mathar, Oct 21 2006

Mathematica

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

Prog

(Python)
a, an, la = [1], 1, 1
print(la-1, an)
while la < 63:
....dc, di = 0, 0
....while di < la:
........if la%a[di] == 0:
............dc = dc+1
........di = di+1
....an = an+dc
....la, a = la+1, a+[an]
....print(la-1, an) # A.H.M. Smeets, Jan 25 2019

Crossrefs

Cf. A123885.

Sequence in context: A112777 A188972 A047612 * A005242 A323976 A188975

Adjacent sequences: A123883 A123884 A123885 * A123887 A123888 A123889

Keyword

easy,nonn

Author

Leroy Quet, Oct 17 2006

Extensions

Extended by Ray Chandler, Oct 19 2006

More terms from R. J. Mathar, Oct 21 2006

Status

approved