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%I #12 May 30 2024 09:52:55
%S 1,5,25,125,626,3125,15625,78125,390625,1953130,9765625,48828125,
%T 244140625,1220703125,6103515650,30517578125,152587890625,
%U 762939453125,3814697265625,19073486328250,95367431640625,476837158203125,2384185791015625,11920928955078125
%N Expansion of Sum_{k>=0} x^(5^k) / (1 - 5*x^(5^k)).
%H Seiichi Manyama, <a href="/A373281/b373281.txt">Table of n, a(n) for n = 1..1000</a>
%F G.f. A(x) satisfies A(x) = x/(1 - 5*x) + A(x^5).
%F If n == 0 (mod 5), a(n) = 5^n + a(n/5) otherwise a(n) = 5^n.
%F a(n) = Sum_{d|n} d * A054662(d).
%o (PARI) b(n, k) = sumdiv(n, d, (gcd(d, k)==1)*(moebius(d)*k^(n/d)))/(k*n);
%o a(n, k=5) = sumdiv(n, d, d*b(d, k));
%Y Cf. A187767, A373279, A373280, A373282, A373283.
%Y Cf. A000351, A054662, A055457.
%K nonn
%O 1,2
%A _Seiichi Manyama_, May 30 2024
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