A329641 a(n) = gcd(A329638(n), A329639(n)).

0, 1, 1, 2, 1, 4, 1, 6, 1, 5, 1, 10, 1, 16, 2, 6, 1, 1, 1, 18, 1, 18, 1, 22, 1, 46, 1, 22, 1, 10, 1, 30, 14, 82, 2, 1, 1, 256, 2, 22, 1, 1, 1, 66, 1, 226, 1, 46, 1, 1, 8, 130, 1, 1, 1, 70, 2, 748, 1, 42, 1, 1362, 2, 2, 10, 42, 1, 214, 254, 4, 1, 1, 1, 3838, 5, 406, 2, 2, 1, 78, 1, 5458, 1, 26, 2, 12250, 2, 10, 1, 2, 1, 934

Offset: 1

Author

Antti Karttunen, Nov 22 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000 (based on Hans Havermann's factorization of A156552)
• 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. A156552, A323243, A324201, A329610, A329638, A329639, A329640, A329644.

Programs

PARI

A323243(n) = if(1==n,0,sigma(A156552(n)));
A156552(n) = {my(f = factor(n), p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res}; \\ From A156552
A329644(n) = sumdiv(n,d,moebius(n/d)*((2*A156552(d))-A323243(d)));
A329641(n) = { my(t=0,u=0); fordiv(n, d, if((d=A329644(d))>0, t +=d, u -= d)); gcd(u,t); };

Formula

a(n) = gcd(A329638(n), A329639(n)).

a(A324201(n)) = A329610(n).