1,2

a(n) <= 2*a(n-1), with equality iff n is prime or n = 4. - Martin Fuller (martin_n_fuller(AT)btinternet.com), Jun 03 2006

a(4) = 8: the subsets of {1, 2, 3, 4} are {}, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}, {1, 2, 3, 4}. The 16 numbers as the product are 1, 1, 2, 3, 4, 2, 3, 4, 6, 8, 12, 6, 8, 12, 24. There are only 8 distinct numbers: 1, 2, 3, 4, 6, 8, 12, 24.

a(6) = 26: the set {1, 2, 3, 4, 5, 6, 2*3, 2*4, 2*5, ..., 5*6, 2*3*4, 2*3*5, ..., 4*5*6, ..., ...2*3*4*5*6} contains 26 different values: {1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 18, 20, 24, 30, 36, 40, 48, 60, 72, 90, 120, 144, 180, 240, 360, 720}

Cf. A070861, A070863.

Sequence in context: A119311 A112992 A070789 this_sequence A018826 A104899 A057975

Adjacent sequences: A060954 A060955 A060956 this_sequence A060958 A060959 A060960

nonn,nice

Jonas Wallgren (jonwa(AT)ida.liu.se), May 10 2001

More terms from Lior Manor (lior.manor(AT)gmail.com) May 26 2002

a(26)-a(32) from Giovanni Resta (g.resta(AT)iit.cnr.it), Feb 14 2006

More terms from Martin Fuller (martin_n_fuller(AT)btinternet.com), Jun 03 2006