A027430 Number of distinct products i*j*k with 1 <= i < j < k <= n.

0, 0, 1, 4, 10, 16, 29, 42, 60, 75, 111, 126, 177, 206, 238, 274, 361, 396, 507, 554, 613, 677, 838, 883, 1004, 1092, 1198, 1277, 1529, 1590, 1881, 1998, 2133, 2275, 2432, 2518, 2921, 3096, 3278, 3391, 3884, 4014, 4563, 4750, 4938, 5186, 5840, 5987, 6422, 6652

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

References

• Amarnath Murthy, Generalization of partition function introducing Smarandache Factor Partitions, Smarandache Notions Journal, 1-2-3, Vol. 11, 2000.

Links

• David A. Corneth, Table of n, a(n) for n = 1..700 (first 200 terms by T. D. Noe)
• Amarnath Murthy, Generalization of partition function introducing Smarandache Factor Partitions, viXra:1403.0647, 2014.
• David A. Corneth, Pari program

Crossrefs

Cf. A000292, A027425, A088434, A100435, A100436.

Number of terms in row n of A083507.

Cf. A027429, A027428.

Programs

Haskell

import Data.List (nub)
a027430 n = length $ nub [i*j*k | k<-[3..n], j<-[2..k-1], i<-[1..j-1]]
-- Reinhard Zumkeller, Jan 01 2012

Mathematica

nn = 50;
prod = Table[0, {1 + nn^3}];
a[1] = 0;
a[n_] := (Do[prod[[1 + i*j*k]] = 1, {i, 0, n}, {j, i+1, n}, {k, j+1, n}]; Count[Take[prod, 1 + n^3], 1] - 1);
Array[a, nn] (* Jean-François Alcover, Jul 31 2018, after T. D. Noe *)

PARI

\\ See PARI link. David A. Corneth, Jul 31 2018

Python

def A027430(n): return len({i*j*k for i in range(1,n+1) for j in range(1,i) for k in range(1,j)}) # Chai Wah Wu, Oct 16 2023

Formula

a(n) = A027429(n)-1. - T. D. Noe, Jan 16 2007

a(n) <= A000292(n - 2). - David A. Corneth, Jul 31 2018

Extensions

Corrected by David Wasserman, Nov 18 2004