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

1,1

Links

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

Example

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

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`(k<n, 0, x^n),
     add(`if`(d>k, 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 *)

Crossrefs

Cf. A060275.

Sequence in context: A067672 A276710 A181484 * A334911 A305942 A261265

Adjacent sequences: A060289 A060290 A060291 * A060293 A060294 A060295

Keyword

easy,nonn

Author

Naohiro Nomoto, Mar 24 2001

Extensions

Name changed by Robert Israel, Feb 09 2015

Status

approved