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Search: id:A138012
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| A138012 |
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a(n) = number of positive divisors, k, of n where d(k) divides n (where d(k) = number of positive divisors of k). |
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3
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| 1, 2, 1, 2, 1, 3, 1, 3, 2, 3, 1, 6, 1, 3, 1, 3, 1, 5, 1, 4, 1, 3, 1, 8, 1, 3, 2, 4, 1, 4, 1, 3, 1, 3, 1, 9, 1, 3, 1, 6, 1, 4, 1, 4, 2, 3, 1, 8, 1, 3, 1, 4, 1, 5, 1, 6, 1, 3, 1, 11, 1, 3, 2, 3, 1, 4, 1, 4, 1, 4, 1, 12, 1, 3, 2, 4, 1, 4, 1, 8, 2, 3, 1, 11, 1, 3, 1, 6, 1, 7, 1, 4, 1, 3, 1, 10, 1, 3, 2, 4, 1, 4, 1, 6
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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First occurrence of k: 1, 2, 6, 20, 18, 12, 90, 24, 36, 96, 60, 72, 5670, 972, 120, 336, 180, 420, 540, 240, 600, 2352, 360, 480, 900, 3000, 840, 1080, 1260, 720, ..., . - Robert G. Wilson v.
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EXAMPLE
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10 has 4 divisors (1,2,5,10). The number of divisors of each of these divisors of 10 form the sequence (1,2,2,4). Of these, three divide 10: 1,2,2. So a(10) = 3.
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MAPLE
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with(numtheory): a:=proc(n) local div, ct, j: div:=divisors(n): ct:=0: for j to tau(n) do if `mod`(n, tau(div[j]))=0 then ct:=ct+1 else end if end do: ct end proc: seq(a(n), n=1..80); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 14 2008
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MATHEMATICA
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Table[Length[Select[Divisors[n], Mod[n, Length[Divisors[ # ]]] == 0 &]], {n, 1, 100}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com)
f[n_] := Count[Mod[n, DivisorSigma[0, Divisors@n]], 0]; Array[f, 104] - Robert G. Wilson v (rgwv(AT)rgwv.com)
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CROSSREFS
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Cf. A138010, A138011.
Sequence in context: A027352 A029238 A126131 this_sequence A072531 A025818 A079413
Adjacent sequences: A138009 A138010 A138011 this_sequence A138013 A138014 A138015
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KEYWORD
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nonn
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AUTHOR
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Leroy Quet (q1qq2qqq3qqqq(AT)yahoo.com), Feb 27 2008
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EXTENSIONS
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More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com) and Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 29 2008
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