A344877 a(n) = gcd(n, A344875(n)), where A344875 is multiplicative with a(2^e) = 2^(1+e) - 1, and a(p^e) = p^e -1 for odd primes p.

1, 1, 1, 1, 1, 6, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 6, 1, 4, 3, 2, 1, 6, 1, 2, 1, 14, 1, 6, 1, 1, 1, 2, 1, 4, 1, 2, 3, 20, 1, 6, 1, 2, 1, 2, 1, 2, 1, 2, 1, 4, 1, 6, 5, 2, 3, 2, 1, 4, 1, 2, 3, 1, 1, 6, 1, 4, 1, 2, 1, 24, 1, 2, 3, 2, 1, 6, 1, 4, 1, 2, 1, 84, 1, 2, 1, 2, 1, 6, 1, 2, 3, 2, 1, 6, 1, 2, 1, 4, 1, 6, 1, 4, 3

Offset

1,6

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Mathematica

f[2, e_] := 2^(e + 1) - 1; f[p_, e_] := p^e - 1; a[1] = 1; a[n_] := GCD[n, Times @@ f @@@ FactorInteger[n]]; Array[a, 100] (* Amiram Eldar, Jun 03 2021 *)

Prog

(PARI)
A344875(n) = { my(f=factor(n)~); prod(i=1, #f, (f[1, i]^(f[2, i]+(2==f[1, i]))-1)); };
A344877(n) = gcd(n, A344875(n));

Crossrefs

Cf. A344875.

Cf. also A323409.

Sequence in context: A324891 A260340 A040037 * A356156 A356157 A333461

Adjacent sequences: A344874 A344875 A344876 * A344878 A344879 A344880

Keyword

nonn

Author

Antti Karttunen, Jun 03 2021

Status

approved