This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
a(5) = 3 because A093449(5) = 13*14*15.
30 is in the sequence as 30 = 5*6 = 5*(5+1). - _David A. Corneth_, Oct 19 2021
maxNum = 1700; lst = {}; For[i = 1, i <= Sqrt[maxNum], i++, j = i + 1; prod = i*j; While[prod < maxNum, AppendTo[lst, prod]; j++; prod *= j]]; lst = Union[lst]
list(lim)=my(v=List([0]),P,k=1,t); while(1, k++; P=binomial('n+k-1,k)*k!; if(subst(P,'n,1)>lim, break); for(n=1,lim, t=eval(P); if(t>lim, next(2)); listput(v,t))); Set(v) \\ Charles R Greathouse IV, Nov 16 2021
import heapq
from sympy import sieve
def aupton(terms, verbose=False):
p = 6; h = [(p, 2, 3)]; nextcount = 4; aset = {0, 2}
while len(aset) < terms:
(v, s, l) = heapq.heappop(h)
aset.add(v)
if verbose: print(f"{v}, [= Prod_{{i = {s}..{l}}} i]")
if v >= p:
p *= nextcount
heapq.heappush(h, (p, 2, nextcount))
nextcount += 1
v //= s; s += 1; l += 1; v *= l
heapq.heappush(h, (v, s, l))
return sorted(aset)
print(aupton(52)) # Michael S. Branicky, Oct 19 2021
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