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

1,6

Links

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

Prog

(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

Crossrefs

tau is A000005.

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

Inspired by A333995.

Sequence in context: A340581 A345116 A278042 * A211161 A348687 A208101

Adjacent sequences: A338711 A338712 A338713 * A338715 A338716 A338717

Keyword

nonn

Author

N. J. A. Sloane, Nov 11 2020

Status

approved