A324191 Number of divisors of n minus the number of distinct values that A297167 obtains over the divisors > 1 of n: a(n) = A000005(n) - A324190(n).

1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 3, 1, 2, 2, 1, 1, 3, 1, 2, 2, 2, 1, 4, 1, 2, 1, 2, 1, 5, 1, 1, 2, 2, 2, 5, 1, 2, 2, 3, 1, 5, 1, 2, 3, 2, 1, 5, 1, 3, 2, 2, 1, 4, 2, 2, 2, 2, 1, 8, 1, 2, 2, 1, 2, 5, 1, 2, 2, 5, 1, 7, 1, 2, 3, 2, 2, 5, 1, 4, 1, 2, 1, 7, 2, 2, 2, 2, 1, 8, 2, 2, 2, 2, 2, 6, 1, 3, 2, 4, 1, 5, 1, 2, 5

Offset: 1

Author

Antti Karttunen, Feb 19 2019

Keywords

• nonn

Comments

a(p^k) = 1 for all primes p and all exponents k >= 0, because with prime powers there are k divisors larger than 1 and A297167 obtains a distinct value for each one of them.

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, A001221, A001222, A046660, A061395, A297167, A324120, A324179, A324120, A324190, A324192.

Cf. A000961 (positions of ones).

Programs

PARI

A061395(n) = if(1==n, 0, primepi(vecmax(factor(n)[, 1])));
A297167(n) = if(1==n, 0, (A061395(n) + (bigomega(n)-omega(n)) - 1));
A324190(n) = #Set(apply(A297167, select(d -> d>1,divisors(n))));
A324191(n) = (numdiv(n)-A324190(n));

Formula

a(n) = A000005(n) - A324190(n).