A068594 Factorable subsets: the number of proper subsets S of {1,2,...,n} that can be expressed in the form S=A*B, where S is defined to be the set {a(i)*b(j)| a(i) in A, b(j) in B}.

0, 0, 0, 3, 3, 11, 11, 23, 33, 63, 63, 137, 137, 257, 320, 535, 535, 1071, 1071, 2031, 2281, 4073, 4073, 7783, 7908, 14692, 15455, 29277, 29277, 58419, 58419, 107728, 111272, 214440, 215444, 429437, 429437, 842109, 856061, 1609547

Offset

1,4

Links

Table of n, a(n) for n=1..40.

Sean A. Irvine, Java program (github)

Example

a(6)=11, since {4}={2}*{2}, {2,4}={2}*{1,2}, {6}={2}*{3}, {2,6}={2}*{1,3}, {4,6}={2}*{2,3}, {2,4,6}={2}*{1,2,3}, {1,2,4}={1,2}*{1,2}, {3,6}={1,2}*{3}, {1,2,3,6}={1,2}*{1,3}, {2,3,4,6}={1,2}*{2,3}, {1,2,3,4,6}={1,2}*{1,2,3} and no other subsets of {1,2,...,6} can be so factored.

Crossrefs

Sequence in context: A167428 A318961 A309798 * A147175 A147112 A147120

Adjacent sequences: A068591 A068592 A068593 * A068595 A068596 A068597

Keyword

nonn

Author

John W. Layman, Mar 14 2002

Extensions

a(16)-a(40) from Sean A. Irvine, Feb 25 2024

Status

approved