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

1,6

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

Formula

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

Prog

(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));

Crossrefs

Cf. A000005, A001221, A001222, A046660, A061395, A297167, A324120, A324179, A324120, A324190, A324192.

Cf. A000961 (positions of ones).

Sequence in context: A332288 A335450 A372772 * A373957 A238946 A379141

Adjacent sequences: A324188 A324189 A324190 * A324192 A324193 A324194

Keyword

nonn

Author

Antti Karttunen, Feb 19 2019

Status

approved