cp's OEIS Frontend

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

%I A025060 #28 Nov 14 2021 10:12:49
%S A025060 11,14,17,19,20,23,26,27,29,31,32,34,35,36,38,39,41,43,44,46,47,49,50,
%T A025060 51,52,53,54,55,56,59,61,62,63,64,65,66,67,68,69,71,73,74,75,76,77,79,
%U A025060 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
%N A025060 Numbers of the form i*j + j*k + k*i, where 1 <= i < j < k.
%C A025060 A025058 without duplicates.
%C A025060 Non-Idoneal Numbers. [_Artur Jasinski_, Oct 27 2008]
%C A025060 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
%H A025060 Bo Gyu Jeong, <a href="/A025060/b025060.txt">Table of n, a(n) for n = 1..2000</a>
%p A025060 N:= 200: # to get all terms <= N
%p A025060 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
%t A025060 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 *)
%o A025060 (Python)
%o A025060 def aupto(N):
%o A025060     aset = set()
%o A025060     for i in range(1, N-1):
%o A025060         for j in range(i+1, N//i + 1):
%o A025060             p, s = i*j, i+j
%o A025060             for k in range(j+1, (N-p)//s + 1):
%o A025060                 aset.add(p + s*k)
%o A025060     return sorted(aset)
%o A025060 print(aupto(109)) # _Michael S. Branicky_, Nov 14 2021
%Y A025060 Cf. A000926 (complement), A025058, A093669.
%K A025060 nonn
%O A025060 1,1
%A A025060 _Clark Kimberling_