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%I #9 Jul 23 2022 09:56:22
%S 1,0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,
%T 1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,
%U 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
%N a(n) = 1 if A003973(n) is a multiple of A000203(n), otherwise 0.
%H Antti Karttunen, <a href="/A355940/b355940.txt">Table of n, a(n) for n = 1..100000</a>
%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>
%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F a(n) = [A355934(n) == 1], where [ ] is the Iverson bracket.
%t f[p_, e_] := ((q = NextPrime[p])^(e + 1) - 1)/(q - 1); a[1] = 1; a[n_] := If[Divisible[Times @@ f @@@ FactorInteger[n], DivisorSigma[1, n]], 1, 0]; Array[a, 100] (* _Amiram Eldar_, Jul 22 2022 *)
%o (PARI)
%o A003973(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); sigma(factorback(f)); };
%o A355940(n) = !(A003973(n)%sigma(n));
%Y Characteristic function of A355941.
%Y Cf. A000203, A003973, A355934.
%K nonn
%O 1
%A _Antti Karttunen_, Jul 22 2022