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A373281
Expansion of Sum_{k>=0} x^(5^k) / (1 - 5*x^(5^k)).
5
1, 5, 25, 125, 626, 3125, 15625, 78125, 390625, 1953130, 9765625, 48828125, 244140625, 1220703125, 6103515650, 30517578125, 152587890625, 762939453125, 3814697265625, 19073486328250, 95367431640625, 476837158203125, 2384185791015625, 11920928955078125
OFFSET
1,2
LINKS
FORMULA
G.f. A(x) satisfies A(x) = x/(1 - 5*x) + A(x^5).
If n == 0 (mod 5), a(n) = 5^n + a(n/5) otherwise a(n) = 5^n.
a(n) = Sum_{d|n} d * A054662(d).
PROG
(PARI) b(n, k) = sumdiv(n, d, (gcd(d, k)==1)*(moebius(d)*k^(n/d)))/(k*n);
a(n, k=5) = sumdiv(n, d, d*b(d, k));
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 30 2024
STATUS
approved