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Number of numbers of the form i*n with 1 <= i <= n and tau(i*n) = 4.
2

%I #20 Oct 15 2023 01:38:38

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

%H Seiichi Manyama, <a href="/A338713/b338713.txt">Table of n, a(n) for n = 1..10000</a>

%t Table[Count[Table[n i,{i,n}],_?(DivisorSigma[0,#]==4&)],{n,90}] (* _Harvey P. Dale_, Jun 14 2022 *)

%o (PARI) a(n) = sum(i=1, n, numdiv(i*n)==4); \\ _Michel Marcus_, Nov 11 2020

%o (Python)

%o from collections import Counter

%o from sympy import factorint

%o def A338713(n):

%o f = Counter(factorint(n))

%o 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 tau is A000005.

%Y For tau(i*n) = 2, 3, 6, see A010051, A296084, A338714.

%Y Inspired by A333995.

%K nonn

%O 1,5

%A _N. J. A. Sloane_, Nov 11 2020