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%I #12 Jun 16 2022 21:18:51
%S 1,1,2,3,4,2,6,7,8,4,10,3,12,6,1,15,16,8,18,4,6,10,22,2,24,12,26,1,28,
%T 1,30,31,1,16,2,8,36,18,12,1,40,6,42,1,1,22,46,15,48,24,1,12,52,26,10,
%U 7,18,28,58,3,60,30,3,63,1,1,66,16,1,2,70,8,72,36,24,1,3,12,78,15,80,40,82,4,2,42,1,2,88
%N a(n) = gcd(A047994(n), A344005(n)).
%H Antti Karttunen, <a href="/A354985/b354985.txt">Table of n, a(n) for n = 1..20000</a>
%H Antti Karttunen, <a href="/A354985/a354985.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%F a(n) = gcd(A047994(n), A344005(n)).
%F a(n) = gcd(A047994(n), A346607(n)) = gcd(A344005(n), A346607(n)).
%t s[n_] := Module[{m = 1}, While[!Divisible[m*(m + 1), n], m++]; m]; f[p_, e_] := p^e - 1; uphi[n_] := Times @@ f @@@ FactorInteger[n]; uphi[1] = 1; a[n_] := GCD[uphi[n], s[n]]; Array[a, 100] (* _Amiram Eldar_, Jun 16 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 A354985(n) = gcd(A047994(n), A344005(n));
%Y Cf. A047994, A344005, A346607, A354986, A354987.
%Y Cf. also A345992.
%K nonn
%O 1,3
%A _Antti Karttunen_, Jun 16 2022
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