

A324179


Number of distinct values A297167 obtains over divisors > 1 of n, minus number of prime factors of n counted with multiplicity: a(n) = A324190(n)  A001222(n).


5



0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 0
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OFFSET

1,56


COMMENTS

a(n) is zero for all prime powers (A000961), but also for many other numbers.


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) = A324190(n)  A001222(n).
a(n) <= A324192(n).


EXAMPLE

Divisors of 56 larger than 1 are [2, 4, 7, 8, 14, 28, 56]. When A297167 is applied to each, one obtains values: [0, 1, 3, 2, 3, 4, 5], of which 6 values are distinct (as one of them, 3, occurs twice). On the other hand, 56 = 2 * 2 * 2 * 7 has four prime factors in total, thus a(56) = 6  4 = 2.


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))));
A324179(n) = (A324190(n)bigomega(n));


CROSSREFS

Cf. A000961, A001222, A061395, A297112, A297167, A324120, A324190, A324191, A324192.
Sequence in context: A089807 A089810 A214411 * A216577 A096562 A096563
Adjacent sequences: A324176 A324177 A324178 * A324180 A324181 A324182


KEYWORD

nonn


AUTHOR

Antti Karttunen, Feb 19 2019


STATUS

approved



