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A354985
a(n) = gcd(A047994(n), A344005(n)).
3
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, 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, 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
OFFSET
1,3
FORMULA
a(n) = gcd(A047994(n), A344005(n)).
a(n) = gcd(A047994(n), A346607(n)) = gcd(A344005(n), A346607(n)).
MATHEMATICA
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 *)
PROG
(PARI)
A047994(n) = { my(f=factor(n)~); prod(i=1, #f, (f[1, i]^f[2, i])-1); };
A344005(n) = for(m=1, oo, if((m*(m+1))%n==0, return(m))); \\ From A344005
A354985(n) = gcd(A047994(n), A344005(n));
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jun 16 2022
STATUS
approved