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%I #15 Oct 10 2019 15:58:10
%S 1,1,1,2,4,8,6,11,21,51,11,22,133,159,151,328,707,1414,880,1732,3850,
%T 9482,1742,3480,22126,37243,25604,51381,102087,204174,157324,285010,
%U 660221,1285026,262885,547906,3664304,5844380,3927062,8543954,19956539
%N a(1)=1; a(n) = Sum_{1<=k<n, gcd(k,n(n+1)/2)=1} a(k).
%H Robert Israel, <a href="/A125597/b125597.txt">Table of n, a(n) for n = 1..5397</a>
%e The positive integers < 8 and coprime to 8*9/2 = 36 are 1,5,7. So a(8) = a(1)+a(5)+a(7) = 1+4+6 = 11.
%p A[1]:= 1:
%p for n from 2 to 100 do
%p A[n]:= add(A[j],j=select(k -> igcd(k,n*(n+1)/2)=1, [$1..n-1]))
%p od:
%p seq(A[i],i=1..100); # _Robert Israel_, Mar 28 2018
%t f[l_List] := Block[{n = Length[l] + 1},Append[l, Plus @@ l[[Select[Range[n - 1], GCD[ #, n*(n + 1)/2] == 1 &]]]]];Nest[f, {1}, 40] (* _Ray Chandler_, Nov 26 2006 *)
%Y Cf. A125596.
%K nonn
%O 1,4
%A _Leroy Quet_, Nov 26 2006
%E Extended by _Ray Chandler_, Nov 26 2006
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