OFFSET
1,2
COMMENTS
At most one power of a previous term is allowed in the sum. Sequence and the first few terms from Andrew Weimholt. Additional terms from Jud McCranie.
It can be shown that a(n) is even for n >= 2 and a(n+1)/a(n) >= 2. Conjecture: lim_{n->infinity} a(n+1)/a(n) = e and lim_{n->infinity} a(n)/e^(n-1) = 1. - Ya-Ping Lu, Feb 18 2022
PROG
(Python)
from itertools import product, combinations
def adding(S): T = {n}; {T.add(x + n) for x in S}; W.update(T)
N = []; n_max = 10**9; W = set(); print(1, end = ', ')
for n in range(2, n_max, 2):
found = False
for i in range(0, len(N)):
t = max(N[i])*min(N[i])
if t == n:
found = True; M = N[:]; del M[i]; S1 = set()
{S1.add(sum(c)) for L in product(*M) for j in range(1, len(L)+1) for c in set(combinations(L, j))}
adding(S1); N[i].add(n)
if found or n in W: continue
print(n, end = ', '); adding(W); N.append({n}) # Ya-Ping Lu, Feb 18 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Jud McCranie, Sep 15 2006
EXTENSIONS
a(21)-a(22) from Donovan Johnson, Aug 31 2008
Offset corrected by Donovan Johnson, Dec 22 2013
STATUS
approved