A336856 Prime-shifted analog of gcd(d(n), sigma(n)): a(n) = gcd(A000005(n), A003973(n)).

1, 2, 2, 1, 2, 4, 2, 4, 1, 4, 2, 6, 2, 4, 4, 1, 2, 2, 2, 2, 4, 4, 2, 8, 3, 4, 4, 6, 2, 8, 2, 2, 4, 4, 4, 1, 2, 4, 4, 8, 2, 8, 2, 2, 2, 4, 2, 2, 1, 6, 4, 6, 2, 8, 4, 8, 4, 4, 2, 12, 2, 4, 6, 1, 4, 8, 2, 2, 4, 8, 2, 4, 2, 4, 6, 6, 4, 8, 2, 2, 1, 4, 2, 12, 4, 4, 4, 8, 2, 4, 4, 6, 4, 4, 4, 12, 2, 2, 2, 3, 2, 8, 2, 8, 8

Offset: 1

Author

Antti Karttunen, Aug 12 2020

Keywords

• nonn

Links

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

Crossrefs

Cf. A000005, A003961, A003973, A009205, A336837, A336838, A336839, A336840, A336841.

Programs

PARI

A003973(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); sigma(factorback(f)); };
A336856(n) = gcd(numdiv(n), A003973(n));

Formula

a(n) = A009205(A003961(n)).

a(n) = gcd(A000005(n), A003973(n)) = gcd(A000005(n), A336841(n)).

a(n) = gcd(A000005(n), 2*A336840(n)).

a(n) = A003973(n) / A336838(n) = A000005(n) / A336839(n).

For n > 1, a(n) = A336841(n) / A336837(n).

For all primes p, and n >= 0, a(p^((2^n)-1)) = 2^n.