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Expansion of Sum_{k>=0} x^(7^k) / (1 - 7*x^(7^k)).
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%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