A123953 - OEIS

A123953

a(0)=1. a(n) = number of terms among terms a(0) through a(n-1) of the sequence which are coprime to n(n+1)/2.

1, 1, 2, 2, 2, 5, 6, 3, 3, 5, 8, 4, 4, 13, 9, 3, 9, 11, 12, 9, 4, 12, 21, 6, 4, 22, 14, 6, 12, 14, 15, 14, 5, 17, 25, 5, 10, 37, 23, 6, 14, 22, 23, 20, 7, 21, 44, 14, 13, 33, 25, 13, 24, 35, 23, 16, 17, 39, 58, 13, 14, 61, 35, 20, 20, 26, 43, 33, 19, 27, 48, 25, 26, 72, 37, 17, 32, 35

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

Table of n, a(n) for n=0..77.

EXAMPLE

Among terms a(0),a(1),...a(8) there are 5 terms coprime to 9*10/2 = 45. (These terms are a(0)=1, a(1)=1, a(2)=2, a(3)=2 and a(4)=2.) So a(9) = 5.

MATHEMATICA

f[l_List] := Block[{n = Length[l]}, Append[l, Length @ Select[l, GCD[n*(n + 1)/2, # ] == 1 &]]]; Nest[f, {1}, 80] (* Ray Chandler, Jun 29 2008 *)

a[0] = 1; a[n_] := a[n] = Count[ GCD[ Table[ a[i], {i, 0, n - 1}], n(n + 1)/2], 1]; Table[ a[n], {n, 0, 77}] (* Robert G. Wilson v *)

CROSSREFS

Cf. A119989.