A364224 - OEIS

A364224

Expansion of Sum_{k>=0} 7^k * x^(7^k) / (1 - x^(7^k))^2.

1, 2, 3, 4, 5, 6, 14, 8, 9, 10, 11, 12, 13, 28, 15, 16, 17, 18, 19, 20, 42, 22, 23, 24, 25, 26, 27, 56, 29, 30, 31, 32, 33, 34, 70, 36, 37, 38, 39, 40, 41, 84, 43, 44, 45, 46, 47, 48, 147, 50, 51, 52, 53, 54, 55, 112, 57, 58, 59, 60, 61, 62, 126, 64, 65, 66, 67, 68, 69, 140, 71, 72, 73, 74, 75, 76, 154

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Table of n, a(n) for n=1..77.

FORMULA

a(n) = n * (A214411(n) + 1).

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

From Amiram Eldar, Jul 14 2023: (Start)

Multiplicative with a(7^e) = (e+1)*7^e and a(p^e) = p*e if p != 7.

Dirichlet g.f.: (7^s/(7^s-7)) * zeta(s-1).

Sum_{k=1..n} a(k) ~ (7/12)*n^2. (End)