A345882 Number of numbers expressible as b(1)*b(2)*...*b(n) with 1 <= b(i) <= i for each i.
1, 2, 5, 11, 30, 64, 178, 382, 758, 1367, 3620, 7193, 19707, 40867, 75706, 130017, 339506, 667390, 1824656, 3724917, 6785689, 11545898, 30099090, 58833294, 105348580, 176098677, 282847446, 438090287, 1095200628, 2057512312, 5494259815, 10925293558, 19311381148
Offset: 1
Examples
For n=3, b(1) must equal 1, b(2) can be 1 or 2, and b(3) can be 1, 2 or 3. This gives 3!=6 possible products: 1*1*1=1, 1*2*1=2, 1*1*2=2, 1*1*3=3, 1*2*2=4 and 1*2*3=6. Since 1*2*1=1*1*2, this process yields 5 distinct numbers, so a(3)=5.
Programs
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Mathematica
list[1] := {1}; list[n_] := list[n] = DeleteDuplicates[Flatten[Table[i*list[n - 1], {i, 1, n}]]]; a[n_] := a[n] = Length[list[n]]; Table[a[n], {n, 1, 10}] -
PARI
a(n) = my(l = List()); forvec(x = vector(n, i, [1, i]), listput(l, prod(i = 1, n, x[i])), 1); listsort(l, 1); #l \\ David A. Corneth, Sep 18 2021
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Python
def A345882set(n): if n == 1: return {1} else: s = A345882set(n-1) c = set(s) for x in s: for i in range(2,n+1): c.add(i*x) return c def A345882(n): return len(A345882set(n)) # Chai Wah Wu, Sep 19 2021
Extensions
a(26)-a(28) from Chai Wah Wu, Sep 19 2021
a(29)-a(33) from Martin Ehrenstein, Sep 22 2021
Comments