A049829 a(n) = Sum_{k=1..n} T(n,k), array T as in A049828.

0, 0, 1, 1, 5, 3, 10, 12, 14, 16, 33, 21, 41, 45, 46, 50, 74, 72, 99, 83, 97, 111, 158, 120, 148, 176, 181, 185, 243, 191, 262, 254, 282, 314, 313, 293, 363, 391, 418, 386, 480, 414, 529, 497, 501, 573, 660, 570, 626, 672, 699, 703

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A049828.

Programs

Maple

T:=  proc(n,k) option remember;
if n*k = 0 then 0 else (n mod k) + procname(k,n mod k) fi
end proc:
seq(add(T(n,k),k=1..n), n=1..100); # Robert Israel, Aug 31 2015

Mathematica

T[n_, k_] := T[n, k] = If[n*k == 0, 0, Mod[n, k] + T[k, Mod[n, k]]];
a[n_] := Sum[T[n, k], {k, 1, n}];
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Sep 16 2022, after Robert Israel *)

PARI

t(n, k) = {x = n; y = k; r = 1; s = 0; while (r, q = x\y; r = x - y*q; s +=r; x = y; y = r;); s;}
a(n) = sum(k=1, n, t(n, k)); \\ Michel Marcus, Aug 31 2015