A351556 a(n) = gcd(n, A019565(n)).

1, 1, 1, 3, 1, 5, 3, 1, 1, 1, 1, 1, 1, 1, 7, 15, 1, 1, 3, 1, 5, 1, 11, 1, 1, 1, 1, 3, 7, 1, 15, 1, 1, 1, 1, 1, 1, 1, 1, 39, 1, 1, 21, 1, 1, 5, 1, 1, 1, 1, 1, 3, 13, 1, 3, 55, 7, 1, 1, 1, 5, 1, 1, 21, 1, 1, 3, 1, 17, 1, 5, 1, 1, 1, 1, 3, 1, 7, 3, 1, 1, 1, 1, 1, 1, 85, 1, 3, 11, 1, 3, 7, 1, 1, 1, 5, 1, 1, 1, 3, 5, 1, 51, 1, 13, 7

Offset: 0

Author

Antti Karttunen, Feb 19 2022

Keywords

• nonn
• look

Links

• Antti Karttunen, Table of n, a(n) for n = 0..65537
• Index entries for sequences related to binary expansion of n
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A007947, A019565.

Cf. also A324198, A351549, A351557, A351558.

Programs

Mathematica

Table[GCD[n, Times @@ Prime@ Flatten@ Position[Reverse@ IntegerDigits[n, 2], 1]], {n, 0, 105}] (* Michael De Vlieger, Feb 20 2022 *)

PARI

A019565(n) = { my(m=1, p=1); while(n>0, p = nextprime(1+p); if(n%2, m *= p); n >>= 1); (m); };
A351556(n) = gcd(n, A019565(n));

Formula

a(n) = gcd(n, A019565(n)) = gcd(A007947(n), A019565(n)).

a(n) = A007947(a(n)).

a(n) = A019565(A351558(n)).