A353645 a(1) = 1, and for n > 1, number of ways to write the square of n as a product of at least two factors, the largest two of which are equal.

1, 1, 1, 2, 1, 2, 1, 4, 2, 3, 1, 5, 1, 3, 2, 7, 1, 5, 1, 6, 2, 3, 1, 10, 2, 3, 4, 6, 1, 8, 1, 12, 3, 3, 2, 15, 1, 3, 3, 12, 1, 9, 1, 7, 5, 3, 1, 21, 2, 6, 3, 7, 1, 13, 2, 12, 3, 3, 1, 21, 1, 3, 5, 21, 2, 11, 1, 8, 3, 7, 1, 35, 1, 3, 5, 8, 2, 12, 1, 23, 7, 3, 1, 25, 2, 3, 3, 15, 1, 21, 2, 8, 3, 3, 2, 43, 1, 6, 6, 16

Offset

1,4

Links

Antti Karttunen, Table of n, a(n) for n = 1..16415

Formula

a(n) = A325045(A000290(n)).

Example

For n=6, 6^2 = 36 can be factorized in two ways so that two largest factors are equal, as 2*2*3*3 = 6*6, therefore a(6) = 2. See also the examples in A325045.

Prog

(PARI)
A325045(n, m=n, facs=List([])) = if(1==n, (0==#facs || (#facs>=2 && facs[1]==facs[2])), my(s=0, newfacs); fordiv(n, d, if((d>1)&&(d<=m), newfacs = List(facs); listput(newfacs, d); s += A325045(n/d, d, newfacs))); (s));
A353645(n) = A325045(n^2);

Crossrefs

Cf. A000290, A325045.

Sequence in context: A180229 A356230 A304576 * A249029 A075997 A244517

Adjacent sequences: A353642 A353643 A353644 * A353646 A353647 A353648

Keyword

nonn

Author

Antti Karttunen, May 03 2022

Status

approved