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%I #20 Jan 08 2023 11:25:40
%S 1,1,1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0,1,0,0,1,0,0,0,1,0,0,1,1,0,0,
%T 0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,0,
%U 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,0,0
%N a(n) = 1 if sigma(2n) - sigma(n) is a power of 2, otherwise 0.
%C a(n) = 1 if n is a squarefree product of Mersenne primes (A000668) multiplied by a power of 2, otherwise 0.
%C c(n) = a(n)*A000035(n) is the characteristic function of A046528.
%H Antti Karttunen, <a href="/A336923/b336923.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) = A209229(A062731(n)-A000203(n)).
%F a(n) = 1 iff A336922(n) = 0, i.e., when A331410(n) is equal to A005087(n).
%F From _Antti Karttunen_, Jan 08 2023: (Start)
%F Multiplicative with a(2^e) = 1, and for odd primes p, a(p^e) = A209229(p+1) if e = 1, and 0 if e > 1.
%F Multiplicative with a(p^e) = [p==2] + (A036987(p)*[e==1]), where [ ] is the Iverson bracket.
%F a(n) = A209229(A002131(n)) = A209229(A054785(n)).
%F (End)
%o (PARI)
%o A209229(n) = (n && !bitand(n,n-1));
%o A336923(n) = A209229(sigma(n+n)-sigma(n));
%o (PARI) A336923(n) = { my(f=factor(n)); prod(k=1,#f~,(2==f[k,1] || A209229(f[k,1]+1)*(1==f[k,2]))); }; \\ _Antti Karttunen_, Jan 06 2023
%Y Characteristic function of A054784.
%Y Cf. A000035, A000203, A000668, A002131, A005087, A036987, A046528, A054785, A062731, A209229, A331410, A335430, A336922, A359579 (Dirichlet inverse).
%Y Cf. also A336477 (analogous sequence for Fermat primes).
%K nonn,mult
%O 1
%A _Antti Karttunen_, Aug 09 2020
%E Keyword:mult added by _Antti Karttunen_, Jan 06 2023
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