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a(n) = 1 if A047994(n) is equal to A344005(n), otherwise 0.
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%I #12 Jun 13 2022 16:47:24

%S 1,1,1,1,1,1,1,1,1,1,1,0,1,1,0,1,1,1,1,0,0,1,1,0,1,1,1,0,1,0,1,1,0,1,

%T 0,0,1,1,0,0,1,0,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,0,1,0,0,1,0,

%U 0,0,1,0,1,1,0,0,0,0,1,0,1,1,1,0,0,1,0,0,1,0,0,0,0,1,0,0,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0,0,1,0,0,1

%N a(n) = 1 if A047994(n) is equal to A344005(n), otherwise 0.

%H Antti Karttunen, <a href="/A354924/b354924.txt">Table of n, a(n) for n = 1..100000</a>

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>

%F a(n) = 1 if A346607(n) = 0, otherwise 0.

%t f[p_, e_] := p^e - 1; uphi[n_] := Times @@ f @@@ FactorInteger[n]; uphi[1] = 1; a[n_] := Module[{m = 1, u = uphi[n]}, While[m <= u && ! Divisible[m*(m + 1), n], m++]; If[m == u, 1, 0]]; Array[a, 100] (* _Amiram Eldar_, Jun 13 2022 *)

%o (PARI)

%o A047994(n) = { my(f=factor(n)~); prod(i=1, #f, (f[1, i]^f[2, i])-1); };

%o A344005(n) = for(m=1, oo, if((m*(m+1))%n==0, return(m))); \\ From A344005

%o A354924(n) = (A047994(n)==A344005(n));

%Y Characteristic function of A354928. Positions of zeros in A346608.

%Y Cf. A047994, A344005, A346607.

%K nonn

%O 1

%A _Antti Karttunen_, Jun 13 2022