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A045619
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Numbers that are the products of 2 or more consecutive integers.
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17
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0, 2, 6, 12, 20, 24, 30, 42, 56, 60, 72, 90, 110, 120, 132, 156, 182, 210, 240, 272, 306, 336, 342, 360, 380, 420, 462, 504, 506, 552, 600, 650, 702, 720, 756, 812, 840, 870, 930, 990, 992, 1056, 1122, 1190, 1260, 1320, 1332, 1406, 1482, 1560, 1640, 1680
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OFFSET
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1,2
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COMMENTS
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Erdős and Selfridge proved that, apart from the first term, these are never perfect powers (A001597). - T. D. Noe, Oct 13 2002
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LINKS
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FORMULA
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Since the oblong numbers (A002378) have relative density of 100%, we have a(n) ~ (n-1) n ~ n^2. - Daniel Forgues, Mar 26 2012
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EXAMPLE
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MATHEMATICA
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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]
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PROG
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(Python)
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)
(PARI) 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
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CROSSREFS
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KEYWORD
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easy,nonn,nice
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AUTHOR
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), Jul 20 2000
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STATUS
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approved
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