A110713 - OEIS

%I #50 Sep 20 2021 21:58:33

%S 1,3,10,25,91,196,750,1485,3025,5566,23387,38402,163268,284376,500004,

%T 795549,3575781,5657839,25413850,40027130,66010230,105164280,

%U 490429875,713491350,1232253906

%N a(n) is the number of distinct products b_1*b_2*...*b_n where 1 <= b_i <= n.

%C If * is changed to + the result is A002061. - _Michel Marcus_ and _David Galvin_, Sep 19 2021

%H Gerhard Kirchner, <a href="/A110713/a110713.pdf">Theory and aspects of extension</a>

%e a(2) = A027424(2) = 3.

%e a(3) = A027425(3) = 10.

%e a(4) = A100437(4) = 25.

%o (PARI) a(n) = my(l = List()); forvec(x = vector(n, i, [1,n]), listput(l, prod(i = 1, n, x[i])), 1); listsort(l, 1); #l \\ _David A. Corneth_, Jan 02 2019

%o (Python)

%o from math import prod

%o from itertools import combinations_with_replacement

%o def A110713(n): return len({prod(d) for d in combinations_with_replacement(list(range(1,n+1)),n)}) # _Chai Wah Wu_, Sep 19 2021

%Y Main diagonal of A322967.

%Y Cf. A110713, A027424, A027425, A100437, A345882.

%K nonn,more

%O 1,2

%A _Jonas Wallgren_, Sep 15 2005

%E a(10)-a(15) from _Donovan Johnson_, Dec 08 2009

%E a(16)-a(25) from _Gerhard Kirchner_, Dec 07 2015