A351557 a(n) = gcd(sigma(n), A019565(n)).

1, 3, 2, 1, 2, 3, 2, 1, 1, 3, 6, 7, 14, 3, 6, 1, 2, 3, 2, 1, 2, 3, 6, 1, 1, 21, 2, 7, 10, 3, 2, 1, 2, 3, 6, 13, 2, 15, 2, 1, 14, 3, 2, 7, 26, 3, 6, 1, 1, 3, 6, 1, 2, 15, 6, 1, 2, 3, 6, 7, 2, 3, 26, 1, 2, 3, 34, 1, 2, 3, 6, 1, 2, 3, 2, 35, 2, 21, 10, 1, 11, 3, 6, 1, 2, 33, 30, 1, 2, 3, 14, 7, 2, 3, 30, 1, 2, 3, 78

Offset: 1

Author

Antti Karttunen, Feb 19 2022

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences related to binary expansion of n
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A007947, A019565, A080398.

Cf. also A324644, A351549, A351556, A351559.

Programs

Mathematica

Table[GCD[DivisorSigma[1, n], Times @@ Prime@ Flatten@ Position[Reverse@ IntegerDigits[n, 2], 1]], {n, 99}] (* 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); };
A351557(n) = gcd(sigma(n), A019565(n));

Formula

a(n) = gcd(A000203(n), A019565(n)) = gcd(A080398(n), A019565(n)).

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

a(n) = A019565(A351559(n)).