A379570 Number of n-digit numbers that have exactly 8 divisors.

0, 10, 170, 1934, 20067, 202246, 2003991, 19674052, 192215670, 1873532828, 18242642732, 177582019015, 1728951136938, 16840198807124, 164117159854744, 1600427660469575, 15617400806292160

Offset: 1

Author

Seiichi Manyama, Dec 26 2024

Keywords

• nonn
• more
• base

Comments

A number has exactly 8 divisors iff it can be expressed as p*q*r, p^3*q, or p^7, where p, q, and r are distinct primes. - David Radcliffe, Dec 30 2024

Links

• Lucas A. Brown, Python program.

Crossrefs

Column k=8 of A284398.

Cf. A215218.

Programs

Python

# See LINKS.

Formula

Sum_{k=1..n} a(k) = A215218(n) + Sum_{p prime} PrimePi[N/p^3] - PrimePi[N^(1/4)] + PrimePi[N^(1/7)] where N = 10^n. - David Radcliffe, Dec 30 2024

Extensions

a(10) from Giorgos Kalogeropoulos, Dec 30 2024

a(11)-a(17) from David Radcliffe, Jan 01 2025