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A080257
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Numbers having at least two distinct or a total of at least three prime factors.
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23
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6, 8, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100
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internal format)
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OFFSET
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1,1
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COMMENTS
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Also numbers greater than the square of their smallest prime-factor: a(n)>A020639(a(n))^2=A088377(a(n));
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LINKS
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FORMULA
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EXAMPLE
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8=2*2*2 and 10=2*5 are terms; 4=2*2 is not a term.
The sequence of terms together with their prime indices begins:
6: {1,2}
8: {1,1,1}
10: {1,3}
12: {1,1,2}
14: {1,4}
15: {2,3}
16: {1,1,1,1}
18: {1,2,2}
20: {1,1,3}
21: {2,4}
22: {1,5}
24: {1,1,1,2}
26: {1,6}
27: {2,2,2}
28: {1,1,4}
30: {1,2,3}
32: {1,1,1,1,1}
(End)
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MATHEMATICA
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Select[Range[100], PrimeNu[#]>1||PrimeOmega[#]>2&] (* Harvey P. Dale, Jul 23 2013 *)
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PROG
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(Haskell)
a080257 n = a080257_list !! (n-1)
a080257_list = m a024619_list a033942_list where
m xs'@(x:xs) ys'@(y:ys) | x < y = x : m xs ys'
| x == y = x : m xs ys
| x > y = y : m xs' ys
(PARI) is(n)=omega(n)>1 || isprimepower(n)>2
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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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