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.
a265125 n = a265125_list !! (n-1) a265125_list = scanl1 (*) a265111_list
Triangle begins 1; 2; 3; 2, 2; 5; 2, 3; 7; 2, 2, 2; 3, 3; 2, 5; 11; 2, 2, 3; ...
import Data.List (unfoldr) a027746 n k = a027746_tabl !! (n-1) !! (k-1) a027746_tabl = map a027746_row [1..] a027746_row 1 = [1] a027746_row n = unfoldr fact n where fact 1 = Nothing fact x = Just (p, x `div` p) where p = a020639 x -- Reinhard Zumkeller, Aug 27 2011
P:=proc(n) local FM: FM:=ifactors(n)[2]: seq(seq(FM[j][1],k=1..FM[j][2]),j=1..nops(FM)) end: 1; for n from 2 to 45 do P(n) od; # yields sequence in triangular form; Emeric Deutsch, Feb 13 2005
row[n_] := Flatten[ Table[#[[1]], {#[[2]]}] & /@ FactorInteger[n]]; Flatten[ Table[ row[n], {n, 1, 45}]] (* Jean-François Alcover, Dec 01 2011 *)
A027746_row(n,o=[1])=if(n>1,concat(apply(t->vector(t[2],i,t[1]), Vec(factor(n)~))),o) \\ Use %(n,[]) if you want the more natural [] for the first row. - M. F. Hasler, Jul 29 2015
def factors(n: int) -> list[int]:
p = n
L:list[int] = []
for f in range(2, p + 1):
if f * f > p: break
while True:
q, r = divmod(p, f)
if r != 0: break
L.append(f)
p = q
if p == 1: return L
L.append(p)
return L # Peter Luschny, Jul 18 2024
v=[1] for k in [2..45]: v.extend(p for (p, m) in factor(k) for _ in range(m)) print(v) # Giuseppe Coppoletta, Dec 29 2017
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