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A161769
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A positive integer n is included if the greatest common divisor of (the sum of the distinct primes dividing n) and (the sum of the exponents in the prime-factorization of n) is > 1.
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0
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4, 15, 16, 21, 27, 28, 33, 35, 39, 42, 48, 51, 52, 55, 57, 60, 64, 65, 69, 72, 76, 77, 78, 84, 85, 87, 90, 91, 93, 95, 98, 105, 108, 110, 111, 114, 115, 119, 120, 123, 124, 126, 129, 132, 133, 135, 140, 141, 143, 145, 148, 150, 155, 156, 159, 161, 162, 170, 172, 175
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| n is included if A161606(n) is >= 2.
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EXAMPLE
| The prime factorization of 28 is 2^2 * 7^1. The sum of the distinct prime divisors of 28 is 2+7 = 9. The sum of the prime-factorization exponents of 28 is 2+1 = 3. Since GCD(9,3) = 3 is > 1, then 28 is included in this sequence.
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MATHEMATICA
| okQ[n_]:=Module[{fitr=Transpose[FactorInteger[n]]}, GCD[Plus@@First[fitr], Plus@@Last[fitr]]>1]; Select[Range[500], okQ] [From Harvey P. Dale (hpd1(AT)nyu.edu), Jan 24 2010]
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CROSSREFS
| A008472, A001222, A161606
Sequence in context: A076349 A175959 A152442 * A135658 A066862 A103540
Adjacent sequences: A161766 A161767 A161768 * A161770 A161771 A161772
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KEYWORD
| nonn
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AUTHOR
| Leroy Quet, Jun 18 2009
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EXTENSIONS
| Additional terms provided Harvey P. Dale (hpd1(AT)nyu.edu), Jan 24 2010
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