A351558 a(n) = A048675(gcd(n, A019565(n))).

0, 0, 0, 2, 0, 4, 2, 0, 0, 0, 0, 0, 0, 0, 8, 6, 0, 0, 2, 0, 4, 0, 16, 0, 0, 0, 0, 2, 8, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 34, 0, 0, 10, 0, 0, 4, 0, 0, 0, 0, 0, 2, 32, 0, 2, 20, 8, 0, 0, 0, 4, 0, 0, 10, 0, 0, 2, 0, 64, 0, 4, 0, 0, 0, 0, 2, 0, 8, 2, 0, 0, 0, 0, 0, 0, 68, 0, 2, 16, 0, 2, 8, 0, 0, 0, 4, 0, 0, 0, 2, 4, 0, 66

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. A004198, A007947, A019565, A087207, A351556.

Cf. also A324198, A351559.

Programs

Mathematica

Table[If[# == 1, 0, Total[#2*2^PrimePi[#1] & @@@ FactorInteger[#]]/2] &@ GCD[n, Times @@ Prime@ Flatten@ Position[Reverse@ IntegerDigits[n, 2], 1]], {n, 102}] (* 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); };
A048675(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; };
A351558(n) = A048675(gcd(n, A019565(n)));

Formula

a(n) = A048675(A351556(n)) = A048675(gcd(n, A019565(n))).

a(n) = n AND A087207(n), where AND is bitwise-and, A004198.