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%I #19 Oct 15 2023 01:38:46
%S 0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,1,0,1,1,1,0,1,0,0,0,
%T 0,0,1,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,1,1,0,1,0,0,1,0,1,0,0,1,0,0,1,1,
%U 0,0,1,0,1,0,0,0,0,0,1,0,1,0,1,0,0,0,0,0,1,0,1,0,0,0,0,0,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,0,0
%N a(1) = 0 and for n > 1, a(n) = 1 if tau(n)-1 divides sigma(n)-1, 0 otherwise. Here tau = A000005, sigma = A000203.
%C Also number of numbers of the form i*n with 1 <= i <= n and tau(i*n) = 3 (equivalently, i*n is the square of a prime). - _N. J. A. Sloane_, Nov 11 2020
%H Antti Karttunen, <a href="/A296084/b296084.txt">Table of n, a(n) for n = 1..65537</a>
%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>
%F a(n) = 1 iff A296082(n) = 1.
%t Join[{0},Table[If[Divisible[DivisorSigma[1,n]-1,DivisorSigma[0,n]-1],1,0],{n,2,120}]] (* _Harvey P. Dale_, Dec 15 2018 *)
%o (PARI) A296084(n) = if(1==n,0,!((sigma(n)-1)%(numdiv(n)-1)));
%o (Python)
%o from math import prod
%o from sympy import factorint
%o def A296084(n):
%o f = factorint(n).items()
%o return int(not (prod((p**(e+1)-1)//(p-1) for p,e in f)-1)%(prod(e+1 for p,e in f)-1)) if n>1 else 0 # _Chai Wah Wu_, Oct 14 2023
%Y Cf. A000005, A000203, A032741, A039653, A296082.
%Y Characteristic function of A284288.
%K nonn
%O 1
%A _Antti Karttunen_, Dec 05 2017