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%I A353633 #19 May 07 2022 16:33:25
%S A353633 1,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,
%T A353633 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U A353633 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1
%N A353633 a(n) = 1 if A351546(n) is a unitary divisor of n, otherwise 0. Here A351546(n) is the largest unitary divisor of sigma(n) coprime with A003961(n).
%C A353633 For all known triperfect numbers, n = 1..6, a(A005820(n)) = 1.
%C A353633 For all known 5-multiperfect numbers, n = 1..65, a(A046060(n)) = 1.
%C A353633 For all known multiperfects m such that sigma(m) is also multiperfect, n = 1..23, a(A323653(n)) = 1.
%C A353633 Observation: Apparently, for no other odd terms than 1 of A006872, a(2*A006872(n)) = 1.
%H A353633 Antti Karttunen, <a href="/A353633/b353633.txt">Table of n, a(n) for n = 1..100000</a>
%H A353633 <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>
%H A353633 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A353633 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A353633 a(n)) = [1 == A353668(n)] * [1 == gcd(A351546(n),A353667(n))], where [ ] are the Iverson brackets.
%o A353633 (PARI)
%o A353633 A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A353633 A351546(n) = { my(f=factor(sigma(n)),u=A003961(n)); prod(k=1,#f~,f[k,1]^((0!=(u%f[k,1]))*f[k,2])); };
%o A353633 A353633(n) =  { my(u=A351546(n)); (!(n%u) && 1==gcd(u,n/u)); };
%Y A353633 Characteristic function of A351551.
%Y A353633 Cf. A000203, A003961, A005820, A351546, A353667, A353668.
%Y A353633 Cf. also A005820, A006872, A046060, A323653.
%K A353633 nonn
%O A353633 1
%A A353633 _Antti Karttunen_, May 04 2022

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