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A156239
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Smallest octagonal number with n distinct prime factors.
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4
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8, 21, 280, 1680, 38760, 326040, 10986360, 185040240, 4897368840, 383246454360, 13143876816840, 376306806515640, 27961718389364760, 3250163645572822440, 152582219844376633080, 6202664616058189439160, 1454199694916714984358120
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OFFSET
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1,1
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COMMENTS
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LINKS
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EXAMPLE
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a(9) = 4897368840 = 2^3*3*5*7*13*17*23*31*37. 4897368840 is the smallest octagonal number with 9 distinct prime factors.
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MATHEMATICA
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f[n_] := PrimeNu@ n; nn = 10; k = 1; t = Table[0, {nn}]; While[Times@@t == 0, oct = k(3k-2); a = f@ oct; If[ a <= nn && t[[a]] == 0, t[[a]] = k; Print[{a, oct}]]; k++]; t (* Robert G. Wilson v, Aug 23 2012 *)
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PROG
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(Python)
from sympy import primefactors
def octagonal(n): return n*(3*n - 2)
def a(n):
k = 1
while len(primefactors(octagonal(k))) != n: k += 1
return octagonal(k)
(Python) # faster version using octagonal structure
from sympy import primefactors, primorial
return len(set(primefactors(n)) | set(primefactors(3*n-2)))
def a(n):
k, lb = 1, primorial(n)
while A000567_distinct_factors(k) != n: k += 1
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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