A373281 Expansion of Sum_{k>=0} x^(5^k) / (1 - 5*x^(5^k)).

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

Seiichi Manyama, Table of n, a(n) for n = 1..1000

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));

Crossrefs

Cf. A187767, A373279, A373280, A373282, A373283.

Cf. A000351, A054662, A055457.

Sequence in context: A370546 A097680 A069030 * A111993 A341266 A113996

Adjacent sequences: A373278 A373279 A373280 * A373282 A373283 A373284

Keyword

nonn

Author

Seiichi Manyama, May 30 2024

Status

approved