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A123174
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Least 3-almost prime T whose Merten's function M(T) = n.
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1
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20, 8, 27, 164, 98, 345, 343, 222, 555, 590, 1358, 1388, 1394, 1407, 1406, 1419, 3435, 3231, 3237, 3236, 3245, 3243, 3275, 3282, 3292, 3297, 8163, 8361, 8666, 8662, 8494, 8493, 8538, 8590
(list; graph; refs; listen; history; internal format)
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OFFSET
| -3,1
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FORMULA
| a(n) = Min[T in A014612 and A002321(T) = n].
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EXAMPLE
| a(-3) = 20 = 2^2 * 5 = the first 3-almost prime T for which the Mertens function M(T) = -3.
a(-2) = 8 = 2^3 = the first 3-almost prime T for which the Mertens function M(T) = -2.
a(-1) = 27 = 3^3 = the first 3-almost prime T for which the Mertens function M(T) = -1.
a(0) = 164 = 2^2 * 41 = Min[A014612 INTERSECTION A028442] = the first semiprime T for which the Mertens function M(T) = 0.
a(1) = 98 = 2 * 7^2 = Min[A014612 INTERSECTION A118684] = the first 3-almost prime T for which the Mertens function M(s) = 1.
a(2) = 335 = 3 * 5 * 23 = the first 3-almost prime T for which the Mertens function M(T) = 2.
a(3) = 343 = 7^3 = the first 3-almost prime T for which the Mertens function M(T) = 3.
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MAPLE
| isA014612 := proc(n) option remember ; RETURN( numtheory[bigomega](n) = 3) ; end: A008683 := proc(n) option remember ; numtheory[mobius](n) ; end: A002321 := proc(n) option remember ; add(A008683(k), k=1..n) ; end: A123174 := proc(n) local T; for T from 2 do if isA014612(T) then if A002321(T) = n then RETURN(T) ; fi; fi; od: end: for n from -3 to 30 do printf("%d, ", A123174(n)) ; od: [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 27 2009]
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CROSSREFS
| Cf. A014612, A002321, A028442, A118684.
Sequence in context: A097395 A108967 A097390 * A040384 A078080 A136010
Adjacent sequences: A123171 A123172 A123173 * A123175 A123176 A123177
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KEYWORD
| easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Oct 02 2006
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EXTENSIONS
| Replaced a(2)=335 by 345 and extended to a(30). R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 27 2009
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