A338714 Number of numbers of the form i*n with 1 <= i <= n and tau(i*n) = 6.

0, 0, 0, 1, 1, 2, 1, 1, 3, 2, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 2, 2, 0, 8, 2, 1, 1, 3, 0, 3, 1, 2, 2, 2, 0, 3, 2, 2, 0, 3, 0, 3, 1, 1, 2, 3, 0, 14, 1, 2, 1, 4, 0, 2, 0, 2, 2, 4, 0, 4, 2, 1, 0, 2, 0, 4, 1, 2, 0, 4, 0, 4, 2, 1, 1, 2, 0, 4, 0, 1, 2, 4, 0, 2, 2, 2, 0, 4, 0, 2, 1, 2, 2, 2

Offset: 1

Author

N. J. A. Sloane, Nov 11 2020

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

tau is A000005.

For tau(i*n) = 2, 3, 4, see A010051, A296084, A338713.

Inspired by A333995.

Programs

PARI

a(n) = sum(i=1, n, numdiv(i*n)==6); \\ Michel Marcus, Nov 11 2020

Python

from collections import Counter
from sympy import factorint
def A338714(n):
    f = Counter(factorint(n))
    return sum(1 for i in range(1,n+1) if (l:=tuple(sorted((f+Counter(factorint(i))).values())))==(1,2) or l==(5,)) # Chai Wah Wu, Oct 14 2023