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A338714
Number of numbers of the form i*n with 1 <= i <= n and tau(i*n) = 6.
2
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
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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Nov 11 2020
STATUS
approved