A050521 Number of factorizations of (n,2*n) into pairs (k,l).

1, 1, 1, 3, 1, 7, 1, 10, 4, 7, 1, 33, 1, 7, 9, 28, 1, 39, 1, 33, 9, 7, 1, 133, 4, 7, 15, 33, 1, 91, 1, 80, 9, 7, 9, 229, 1, 7, 9, 133, 1, 91, 1, 33, 53, 7, 1, 474, 4, 39, 9, 33, 1, 175, 9, 133, 9, 7, 1, 569, 1, 7, 53, 208, 9, 91, 1, 33, 9, 91, 1

Offset

1,4

Comments

Pairs (k,l) must satisfy 0<k, 0<l; if k=1 then l=1. Definition of "*": (a,b)*(x,y)=(a*x,b*y); unit is (1,1).

Factorization is up to ordering of pairs, thus (2,2)*(5,10) is the same as (5,10)*(2,2). Factorizations may involve an arbitrary number of pairs, (2,2)*(3,4)*(5,6)=(30,48). - Sean A. Irvine, Mar 21 2013

Links

Giovanni Resta, Table of n, a(n) for n = 1..1000

Example

(10,20) = (2,1)*(5,20) = (2,20)*(5*1) = (2,2)*(5,10) = (2,10)*(5,2) = (2,4)*(5,5) = (2,5)*(5,4); so a(10) = 7.

Crossrefs

Cf. A051707.

Sequence in context: A077202 A086665 A273013 * A266724 A247146 A362628

Adjacent sequences: A050518 A050519 A050520 * A050522 A050523 A050524

Keyword

nonn,nice,easy

Author

Yasutoshi Kohmoto

Extensions

More terms from Sean A. Irvine, Mar 21 2013

Status

approved