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 A138224 a(n) = the nearest divisor of n to the number of positive divisors of n. In case of tie, round down. 4
 1, 2, 1, 2, 1, 3, 1, 4, 3, 5, 1, 6, 1, 2, 3, 4, 1, 6, 1, 5, 3, 2, 1, 8, 1, 2, 3, 7, 1, 6, 1, 4, 3, 2, 5, 9, 1, 2, 3, 8, 1, 7, 1, 4, 5, 2, 1, 8, 1, 5, 3, 4, 1, 9, 5, 8, 3, 2, 1, 12, 1, 2, 7, 8, 5, 6, 1, 4, 3, 7, 1, 12, 1, 2, 5, 4, 1, 6, 1, 10, 3, 2, 1, 12, 5, 2, 3, 8, 1, 10, 1, 4, 3, 2, 5, 12, 1, 7, 3, 10, 1, 6 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS EXAMPLE There are four positive divisors of 15: (1,3,5,15). There are two divisors, 3 and 5, that are nearest 4. We take the smaller divisor, 3 in this case, in case of a tie; so a(15) = 3. MAPLE A138224 := proc(n) if n = 1 then RETURN(1); fi; t := numtheory[tau](n) ; dvs := sort(convert(numtheory[divisors](n), list)) ; a := op(1, dvs) ; for i from 2 to nops(dvs) do if abs(op(i, dvs) - t) < abs(a-t) then a := op(i, dvs) ; fi; od: a ; end: seq(A138224(n), n=1..120) ; # R. J. Mathar, Jul 20 2009 CROSSREFS Cf. A138221, A138222, A138223, A000005. Sequence in context: A029216 A153174 A138222 * A181472 A271825 A271875 Adjacent sequences:  A138221 A138222 A138223 * A138225 A138226 A138227 KEYWORD nonn AUTHOR Leroy Quet, Mar 06 2008 EXTENSIONS Extended beyond a(15) by R. J. Mathar, Jul 20 2009 STATUS approved

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