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

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%I A338714 #16 Oct 15 2023 01:38:33
%S A338714 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,
%T A338714 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,
%U A338714 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
%N A338714 Number of numbers of the form i*n with 1 <= i <= n and tau(i*n) = 6.
%H A338714 Seiichi Manyama, <a href="/A338714/b338714.txt">Table of n, a(n) for n = 1..10000</a>
%o A338714 (PARI) a(n) = sum(i=1, n, numdiv(i*n)==6); \\ _Michel Marcus_, Nov 11 2020
%o A338714 (Python)
%o A338714 from collections import Counter
%o A338714 from sympy import factorint
%o A338714 def A338714(n):
%o A338714     f = Counter(factorint(n))
%o A338714     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
%Y A338714 tau is A000005.
%Y A338714 For tau(i*n) = 2, 3, 4, see A010051, A296084, A338713.
%Y A338714 Inspired by A333995.
%K A338714 nonn
%O A338714 1,6
%A A338714 _N. J. A. Sloane_, Nov 11 2020