A093669 Numbers having a unique representation as ab+ac+bc, with 0 < a < b < c.
11, 14, 17, 19, 20, 27, 32, 34, 36, 43, 46, 49, 52, 64, 67, 73, 82, 97, 100, 142, 148, 163, 193
Offset: 1
Examples
11 is on the list because 11 = 1*2+1*3+2*3.
References
- See A025052.
Crossrefs
Programs
-
Mathematica
oneSol={}; Do[lim=Ceiling[(n-2)/3]; cnt=0; Do[If[n>a*b && Mod[n-a*b, a+b]==0 && Quotient[n-a*b, a+b]>b, cnt++; If[cnt>1, Break[]]], {a, 1, lim-1}, {b, a+1, lim}]; If[cnt==1, AppendTo[oneSol, n]], {n, 10000}]; oneSol -
Python
from collections import Counter def aupto(N): acount = Counter() 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): acount.update([p + s*k]) return sorted([k for k in acount if acount[k] == 1]) print(aupto(10**5)) # Michael S. Branicky, Nov 14 2021
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
Keywords
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
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
Comments