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A156238
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Smallest heptagonal number with n distinct prime factors.
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5
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7, 18, 286, 3010, 32890, 769230, 3333330, 159189030, 16015883940, 477463360374, 21643407275490, 1148540321999070, 18489352726664820, 4561561662153109614, 71000485538666794110, 14440652550858108745170, 927869754030522488795610
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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) = 16015883940 = 2^2*3^2*5*7*17*19*23*29*59. 16015883940 is the smallest heptagonal number with 9 distinct prime factors.
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PROG
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(Python)
from sympy import primefactors
def A000566(n): return n*(5*n-3)//2
def a(n):
k = 1
while len(primefactors(A000566(k))) != n: k += 1
(Python) # faster version using heptagonal structure
from sympy import primefactors
def A000566(n): return n*(5*n-3)//2
pf1 = primefactors(n)
pf2 = primefactors(5*n-3)
combined = set(pf1) | set(pf2)
return len(combined) if n%4 == 0 or (5*n-3)%4 == 0 else len(combined)-1
def a(n):
k = 1
while A000566_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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