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A353337
Number of ways to write n as a product of the terms of A028260 larger than 1; a(1) = 1 by convention (an empty product).
5
1, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 2, 0, 0, 0, 0, 1, 1, 0, 2, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 3, 0, 1, 1, 2, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 2, 1, 2, 1, 1, 0, 3, 0, 1, 0, 3, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 1, 0, 3, 1, 1, 1, 2, 0, 3, 1, 0, 1, 1, 1, 4, 0, 0, 0, 3, 0, 0, 0, 2, 0
OFFSET
1,16
COMMENTS
Number of factorizations of n into factors k > 1 for which there is an even number of primes (when counted with multiplicity, A001222) in their prime factorization.
FORMULA
a(n) = a(A046523(n)). [The sequence depends only on the prime signature of n].
For all n >= 1, a(n) >= A320655(n), and a(n) >= A353377(n).
EXAMPLE
Of the eleven divisors of 96 larger than one, the following: [4, 6, 16, 24, 96] are terms of A028260 because they have an even number of prime factors when counted with repetition. Using them, we can factor 96 in four possible ways, as 96 = 24*4 = 16*6 = 6*4*4, therefore a(96) = 4.
PROG
(PARI)
A065043(n) = (1 - (bigomega(n)%2));
A353337(n, m=n) = if(1==n, 1, my(s=0); fordiv(n, d, if((d>1)&&(d<=m)&&A065043(d), s += A353337(n/d, d))); (s));
CROSSREFS
Cf. also A320655, A353377.
Sequence in context: A334944 A174875 A193510 * A351907 A357374 A264048
KEYWORD
nonn
AUTHOR
Antti Karttunen, Apr 17 2022
STATUS
approved