login
A345061
a(n) = gcd(A071324(n), A206369(n)).
5
1, 1, 2, 3, 4, 2, 6, 5, 7, 2, 10, 2, 12, 2, 4, 11, 16, 1, 18, 12, 4, 2, 22, 2, 21, 2, 20, 18, 28, 2, 30, 21, 4, 2, 8, 1, 36, 2, 4, 4, 40, 4, 42, 30, 4, 2, 46, 2, 43, 1, 4, 36, 52, 20, 8, 2, 4, 2, 58, 8, 60, 2, 2, 43, 8, 4, 66, 48, 4, 6, 70, 7, 72, 2, 2, 54, 12, 8, 78, 4, 61, 2, 82, 18, 8, 2, 4, 10, 88, 4, 12, 66
OFFSET
1,3
LINKS
FORMULA
a(n) = gcd(A071324(n), A206369(n)).
a(n) = gcd(A071324(n), A345060(n)) = gcd(A206369(n), A345060(n)).
a(n) = A071324(n) / A345062(n) = A206369(n) / A345063(n).
MATHEMATICA
{1}~Join~Array[GCD[Total[-#*(-1)^Range[Length[#], 1, -1]] &@ Divisors[#], Times @@ (Sum[(-1)^(#2 - k)*#1^k, {k, 0, #2}] & @@@ FactorInteger[#])] &, 91, 2] (* Michael De Vlieger, Jul 06 2021, after Amiram Eldar at A071324 and A206369 *)
PROG
(PARI)
A071324(n) = my(d=Vecrev(divisors(n))); sum(k=1, #d, (-1)^(k+1)*d[k]); \\ From A071324
A206369(n) = sumdiv(n, d, eulerphi(n/d) * issquare(d)); \\ From A206369
A345061(n) = gcd(A071324(n), A206369(n));
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jun 07 2021
STATUS
approved