A329036 Number of common divisors of n and A122111(n).

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

Offset: 1

Author

Antti Karttunen, Nov 08 2019

Keywords

• nonn

Links

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

Crossrefs

Cf. A000005, A001222, A122111, A280491, A329042, A329043.

Programs

PARI

A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
A122111(n) = if(1==n,n,prime(bigomega(n))*A122111(A064989(n)));
A280491(n) = gcd(n,A122111(n));
A329036(n) = numdiv(A280491(n));

Formula

a(n) = A000005(A280491(n)) = A000005(gcd(n, A122111(n))).

a(n) = 1+A001222(A329042(n)) = 1+A001222(A329043(n)).