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A138010
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a(n) = number of positive divisors of n that each divide d(n). (d(n) = number of positive divisors of n.) a(n) also equals d(GCD(n,d(n))).
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2
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1, 2, 1, 1, 1, 2, 1, 3, 2, 2, 1, 4, 1, 2, 1, 1, 1, 4, 1, 2, 1, 2, 1, 4, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 4, 1, 2, 1, 6, 1, 2, 2, 1, 1, 2, 1, 2, 1, 2, 1, 6, 1, 2, 2, 2, 1, 2, 1, 4, 1, 2, 1, 6, 1, 2, 1, 4, 1, 4, 1, 2, 1, 2, 1, 6, 1, 2, 2, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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EXAMPLE
| 12 has 6 divisors (1,2,3,4,6,12). Those divisors of 12 that divide 6 are 1,2,3,6. Since there are 4 of these, then a(12) = 4.
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MAPLE
| with(numtheory): a:=proc(n) local div, c, j: div:=divisors(n): c:=0: for j to tau(n) do if `mod`(tau(n), div[j])=0 then c:=c+1 else end if end do: c end proc: seq(a(n), n=1..90); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 02 2008
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MATHEMATICA
| Table[Length[Select[Divisors[n], Mod[Length[Divisors[n]], # ] == 0 &]], {n, 1, 100}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Feb 29 2008
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CROSSREFS
| Cf. A138011, A138012.
Sequence in context: A085091 A052128 A114536 * A167204 A104306 A074389
Adjacent sequences: A138007 A138008 A138009 * A138011 A138012 A138013
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KEYWORD
| nonn
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AUTHOR
| Leroy Quet, Feb 27 2008
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EXTENSIONS
| More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com) and Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 29 2008
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