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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.
3
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
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
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jun 03 2021
STATUS
approved