%I #11 May 30 2024 09:52:41
%S 1,7,49,343,2401,16807,117650,823543,5764801,40353607,282475249,
%T 1977326743,13841287201,96889010414,678223072849,4747561509943,
%U 33232930569601,232630513987207,1628413597910449,11398895185373143,79792266297612050,558545864083284007
%N Expansion of Sum_{k>=0} x^(7^k) / (1 - 7*x^(7^k)).
%H Seiichi Manyama, <a href="/A373283/b373283.txt">Table of n, a(n) for n = 1..1000</a>
%F G.f. A(x) satisfies A(x) = x/(1 - 7*x) + A(x^7).
%F If n == 0 (mod 7), a(n) = 7^n + a(n/7) otherwise a(n) = 7^n.
%F a(n) = Sum_{d|n} d * A373277(d).
%o (PARI) b(n, k) = sumdiv(n, d, (gcd(d, k)==1)*(moebius(d)*k^(n/d)))/(k*n);
%o a(n, k=7) = sumdiv(n, d, d*b(d, k));
%Y Cf. A187767, A373279, A373280, A373281, A373282.
%Y Cf. A000420, A373217, A373277.
%K nonn
%O 1,2
%A _Seiichi Manyama_, May 30 2024