A344877 - OEIS

%I #10 Jun 30 2021 19:48:05

%S 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,

%T 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,

%U 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

%N 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.

%H Antti Karttunen, <a href="/A344877/b344877.txt">Table of n, a(n) for n = 1..10000</a>

%H Antti Karttunen, <a href="/A344877/a344877.txt">Data supplement: n, a(n) computed for n = 1..65537</a>

%t 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 *)

%o (PARI)

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

%o A344877(n) = gcd(n, A344875(n));

%Y Cf. A344875.

%Y Cf. also A323409.

%K nonn

%O 1,6

%A _Antti Karttunen_, Jun 03 2021