A110713 - OEIS

A110713

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

1, 3, 10, 25, 91, 196, 750, 1485, 3025, 5566, 23387, 38402, 163268, 284376, 500004, 795549, 3575781, 5657839, 25413850, 40027130, 66010230, 105164280, 490429875, 713491350, 1232253906

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OFFSET

1,2

COMMENTS

If * is changed to + the result is A002061. - Michel Marcus and David Galvin, Sep 19 2021

LINKS

Table of n, a(n) for n=1..25.

Gerhard Kirchner, Theory and aspects of extension

EXAMPLE

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

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

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

PROG

(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

(Python)

from math import prod

from itertools import combinations_with_replacement

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

CROSSREFS

Main diagonal of A322967.

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

Sequence in context: A095052 A196984 A131433 * A098702 A100001 A227937

Adjacent sequences: A110710 A110711 A110712 * A110714 A110715 A110716

KEYWORD

nonn,more

AUTHOR

Jonas Wallgren, Sep 15 2005

EXTENSIONS

a(10)-a(15) from Donovan Johnson, Dec 08 2009

a(16)-a(25) from Gerhard Kirchner, Dec 07 2015

STATUS

approved