A060275 At least two ordered triples of positive numbers have sum n and equal products.

13, 14, 16, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83

Offset: 1

Author

Naohiro Nomoto, Mar 23 2001

Keywords

• easy
• nonn

Comments

Any two such triples are disjoint.

Complement appears to be {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 15, 18}. - Robert Israel, Feb 10 2015

Examples

			13=6+6+1=9+2+2, 6*6*1=9*2*2, so 13 is in the sequence.
		

Programs

Maple

N:= 100: # to get all entries <= N
for i from 1 to N do R[i]:= {} od:
A:= {}:
for a from 1 to floor(N/3) do
  for b from a to floor((N-a)/2) do
    for c from b to N-a-b do
       p:= a*b*c;
       s:= a+b+c;
       if member(p,R[s]) then A:= A union {s}
       else R[s]:= R[s] union {p}
       fi;
od od od:
A;
# if using Maple 11 or earlier, uncomment the next line
# sort(convert(A,list));  # Robert Israel, Feb 10 2015

Extensions

Name changed by Robert Israel, Feb 12 2015