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A140222
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A number n is included if (sum{k=1 to n} d(k)) is prime, where d(k) is the number of divisors of k.
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1
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2, 3, 9, 11, 13, 14, 28, 29, 31, 34, 35, 51, 54, 56, 61, 81, 83, 93, 94, 97, 98, 123, 124, 131, 140, 142, 171, 173, 177, 179, 180, 185, 187, 190, 191, 193, 195, 228, 230, 231, 233, 234, 248, 251, 290, 293, 294, 296, 297, 304, 309, 310, 315, 316, 320, 322, 373
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| sum{k=1 to n} d(k) = sum{k=1 to n} floor(n/k) = A006218(n).
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EXAMPLE
| 9 is in the sequence because the number of divisors of 1,2,...,9 are 1,2,2,3,2,4,2,4,3, respectively, having as sum the prime number 23.
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MAPLE
| with(numtheory): a:=proc(n) if isprime(sum(tau(k), k=1..n))=true then n else end if end proc: seq(a(n), n=1..400); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 08 2008
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CROSSREFS
| Cf. A006218, A140221.
Sequence in context: A057236 A063257 A103039 * A121557 A138984 A110772
Adjacent sequences: A140219 A140220 A140221 * A140223 A140224 A140225
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KEYWORD
| nonn
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AUTHOR
| Leroy Quet May 12 2008
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EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 08 2008
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