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Search: id:A109383
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| A109383 |
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5-almost primes of the form semiprime + 1. |
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+0
5
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| 112, 120, 162, 300, 304, 378, 392, 396, 408, 520, 552, 567, 592, 612, 630, 656, 675, 680, 688, 696, 700, 750, 780, 918, 924, 944, 952, 980, 990, 1044, 1100, 1116, 1136, 1140, 1160, 1168, 1170, 1242, 1264, 1272, 1300, 1323, 1352, 1372, 1380, 1386, 1416, 1470
(list; graph; listen)
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OFFSET
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1,1
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FORMULA
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a(n) is in this sequence iff a(n) is in A014614 and (a(n)-1) is in A001358.
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EXAMPLE
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a(1) = 112 because (3*37)+1 = (2^4) * 7 = 112.
a(2) = 120 because (7*17)+1 = (2^3) * 3 * 5 = 120.
a(3) = 162 because (7*23)+1 = 2 * (3^4) = 162.
a(4) = 300 because (13*23)+1 = (2^2) * 3 * (5^2) = 300.
a(5) = 304 because (3*101)+1 = (2^4) * 19 = 304.
a(6) = 378 because (13*29)+1 = 2 * (3^3) * 7 = 378.
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MATHEMATICA
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f[n_] := Plus @@ Last /@ FactorInteger[n]; Select[Range[1500], f[ # ] == 5 && f[ # - 1] == 2 &] (*Chandler*)
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CROSSREFS
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Primes are in A000040. Semiprimes are in A001358. 5-almost primes are in A014614.
Primes of the form semiprime + 1 are in A005385 (safe primes).
Semiprimes of the form semiprime + 1 are in A109373.
3-almost primes of the form semiprime + 1 are in A109067.
4-almost primes of the form semiprime + 1 are in A109287.
5-almost primes of the form semiprime + 1 are in this sequence.
Least n-almost prime of the form semiprime + 1 are in A128665.
Cf. A077065, A079148, A092307.
Sequence in context: A010032 A129947 A096680 this_sequence A036301 A117723 A157662
Adjacent sequences: A109380 A109381 A109382 this_sequence A109384 A109385 A109386
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Aug 25 2005
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EXTENSIONS
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Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Mar 20 2007
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