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A338713 Number of numbers of the form i*n with 1 <= i <= n and tau(i*n) = 4.

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%I A338713 #20 Oct 15 2023 01:38:38
%S A338713 0,0,1,1,2,1,3,1,1,1,4,0,5,1,1,0,6,0,7,0,1,1,8,0,1,1,1,0,9,0,10,0,1,1,
%T A338713 1,0,11,1,1,0,12,0,13,0,0,1,14,0,1,0,1,0,15,0,1,0,1,1,16,0,17,1,0,0,1,
%U A338713 0,18,0,1,0,19,0,20,1,0,0,1,0,21,0,0,1,22,0,1,1,1,0,23
%N A338713 Number of numbers of the form i*n with 1 <= i <= n and tau(i*n) = 4.
%H A338713 Seiichi Manyama, <a href="/A338713/b338713.txt">Table of n, a(n) for n = 1..10000</a>
%t A338713 Table[Count[Table[n i,{i,n}],_?(DivisorSigma[0,#]==4&)],{n,90}] (* _Harvey P. Dale_, Jun 14 2022 *)
%o A338713 (PARI) a(n) = sum(i=1, n, numdiv(i*n)==4); \\ _Michel Marcus_, Nov 11 2020
%o A338713 (Python)
%o A338713 from collections import Counter
%o A338713 from sympy import factorint
%o A338713 def A338713(n):
%o A338713     f = Counter(factorint(n))
%o A338713     return sum(1 for i in range(1,n+1) if (l:=tuple((f+Counter(factorint(i))).values()))==(1,1) or l==(3,)) # _Chai Wah Wu_, Oct 14 2023
%Y A338713 tau is A000005.
%Y A338713 For tau(i*n) = 2, 3, 6, see A010051, A296084, A338714.
%Y A338713 Inspired by A333995.
%K A338713 nonn
%O A338713 1,5
%A A338713 _N. J. A. Sloane_, Nov 11 2020