A373283 Expansion of Sum_{k>=0} x^(7^k) / (1 - 7*x^(7^k)).

1, 7, 49, 343, 2401, 16807, 117650, 823543, 5764801, 40353607, 282475249, 1977326743, 13841287201, 96889010414, 678223072849, 4747561509943, 33232930569601, 232630513987207, 1628413597910449, 11398895185373143, 79792266297612050, 558545864083284007

Offset: 1

Author

Seiichi Manyama, May 30 2024

Keywords

• nonn

Links

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

Crossrefs

Cf. A187767, A373279, A373280, A373281, A373282.

Cf. A000420, A373217, A373277.

Programs

PARI

b(n, k) = sumdiv(n, d, (gcd(d, k)==1)*(moebius(d)*k^(n/d)))/(k*n);
a(n, k=7) = sumdiv(n, d, d*b(d, k));

Formula

G.f. A(x) satisfies A(x) = x/(1 - 7*x) + A(x^7).

If n == 0 (mod 7), a(n) = 7^n + a(n/7) otherwise a(n) = 7^n.

a(n) = Sum_{d|n} d * A373277(d).