A060292 At least two unordered triples of positive numbers have product n and equal sums.

36, 40, 72, 90, 96, 126, 144, 168, 176, 200, 225, 234, 240, 252, 270, 280, 288, 297, 320, 360, 396, 408, 420, 432, 450, 480, 504, 520, 540, 546, 550, 560, 576, 588, 600, 630, 648, 672, 675, 690, 714, 720, 735, 736, 768, 780, 784, 800, 816, 840, 850, 855

Offset: 1

Author

Naohiro Nomoto, Mar 24 2001

Keywords

• easy
• nonn

Examples

			36=6*6*1=9*2*2. 6+6+1=9+2+2. so 36 is in the sequence.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 160 terms from Carmine Suriano)

Crossrefs

Cf. A060275.

Programs

Maple

N:= 1000: # to get all entries <= N
for i from 1 to N do R[i]:= {} od:
A:= {}:
for a from 1 to floor(N^(1/3)) do
  for b from a to floor((N/a)^(1/2)) do
    for c from b to floor(N/(a*b)) do
       p:= a*b*c;
       s:= a+b+c;
       if member(s,R[p]) then A:= A union {p}
       else R[p]:= R[p] union {s}
       fi;
od od od:
A;
# if using Maple 11 or earlier, uncomment the next line
# sort(convert(A,list)); # Robert Israel, Feb 09 2015
# second Maple program:
b:= proc(n, k, t) option remember; expand(`if`(t=0, `if`(kk, 0, b(n/d, d, t-1)*x^d), d=numtheory[divisors](n))))
    end:
a:= proc(n) option remember; local k; for k from 1+
      `if`(n=1, 0, a(n-1)) while max(coeffs(b(k$2, 2)))<2 do od; k
    end:
seq(a(n), n=1..50);  # Alois P. Heinz, May 16 2020

Mathematica

b[n_, k_, t_] := b[n, k, t] = Expand[If[t == 0, If[k < n, 0, x^n], Sum[If[d > k, 0, b[n/d, d, t - 1] x^d], {d, Divisors[n]}]]];
a[n_] := a[n] = Module[{k}, For[k = 1 + If[n == 1, 0, a[n - 1]], Max[ CoefficientList[b[k, k, 2], x]] < 2, k++]; k];
Array[a, 52] (* Jean-François Alcover, May 30 2020, after Alois P. Heinz *)

Extensions

Name changed by Robert Israel, Feb 09 2015