A353338 Number of ways to write the square of n as a product of the terms of A028260 larger than 1; a(1) = 1 by convention (an empty product).

1, 1, 1, 2, 1, 3, 1, 3, 2, 3, 1, 6, 1, 3, 3, 5, 1, 6, 1, 6, 3, 3, 1, 12, 2, 3, 3, 6, 1, 12, 1, 7, 3, 3, 3, 16, 1, 3, 3, 12, 1, 12, 1, 6, 6, 3, 1, 21, 2, 6, 3, 6, 1, 12, 3, 12, 3, 3, 1, 33, 1, 3, 6, 11, 3, 12, 1, 6, 3, 12, 1, 33, 1, 3, 6, 6, 3, 12, 1, 21, 5, 3, 1, 33, 3, 3, 3, 12, 1, 33, 3, 6, 3, 3, 3, 36, 1, 6, 6

Offset

1,4

Comments

Number of factorizations of n^2 into factors k > 1 for which there is an even number of primes (when counted with multiplicity, A001222) in their prime factorization.

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Index entries for sequences computed from exponents in factorization of n

Formula

a(n) = A353337(A000290(n)).

a(n) = a(A046523(n)). [The sequence depends only on the prime signature of n].

For all n >= 1, a(n) >= A353378(n).

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));
A353338(n) = A353337(n^2);

Crossrefs

Cf. A000290, A001222, A028260, A038548, A046523, A065043, A353337.

Cf. also A353378.

Sequence in context: A325765 A032741 A364818 * A319149 A344462 A321887

Adjacent sequences: A353335 A353336 A353337 * A353339 A353340 A353341

Keyword

nonn

Author

Antti Karttunen, Apr 17 2022

Status

approved