A025060 Numbers of the form i*j + j*k + k*i, where 1 <= i < j < k.

11, 14, 17, 19, 20, 23, 26, 27, 29, 31, 32, 34, 35, 36, 38, 39, 41, 43, 44, 46, 47, 49, 50, 51, 52, 53, 54, 55, 56, 59, 61, 62, 63, 64, 65, 66, 67, 68, 69, 71, 73, 74, 75, 76, 77, 79, 80, 81, 82, 83, 84, 86, 87, 89, 90, 91, 92, 94, 95, 96, 97, 98, 99, 100, 101, 103, 104, 106, 107, 108, 109

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Comments

A025058 without duplicates.

Non-Idoneal Numbers. [Artur Jasinski, Oct 27 2008]

Conjecture: If i, j and k are allowed to be negative, but not zero, and are still distinct, then the sequence is all the integers. - Jon Perry, Apr 21 2013

Links

• Bo Gyu Jeong, Table of n, a(n) for n = 1..2000

Crossrefs

Cf. A000926 (complement), A025058, A093669.

Programs

Maple

N:= 200: # to get all terms <= N
sort(convert({seq(seq(seq(i*j + j*k + i*k, i=1..min(j-1, (N-j*k)/(j+k))),j=2..min(k-1,(N-k)/(1+k))),k=3..(N-2)/3)},list)); # Robert Israel, Sep 06 2016

Mathematica

aa = {}; Do[Do[Do[k = a b + b c + c a; AppendTo[aa, a b + b c + c a], {a, 1, b - 1}], {b, 2, c - 1}], {c, 3, 10}]; Union[aa] (* Artur Jasinski, Oct 27 2008 *)

Python

def aupto(N):
    aset = set()
    for i in range(1, N-1):
        for j in range(i+1, N//i + 1):
            p, s = i*j, i+j
            for k in range(j+1, (N-p)//s + 1):
                aset.add(p + s*k)
    return sorted(aset)
print(aupto(109)) # Michael S. Branicky, Nov 14 2021