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A367632 Numbers k with at least one pair of adjacent divisors i,j of k with i < j such that i' > j'. Here, n' denotes the arithmetic derivative of n. 0
20, 28, 40, 42, 44, 52, 56, 60, 66, 68, 72, 76, 78, 80, 84, 88, 92, 99, 100, 102, 104, 110, 112, 114, 116, 117, 120, 124, 126, 130, 132, 136, 138, 140, 144, 148, 152, 153, 156, 160, 164, 168, 170, 171, 172, 174, 176, 180, 184, 186, 188, 190, 196, 198, 200, 204 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Numbers whose list of arithmetic derivatives of its divisors has at least one descent (in terms of its increasing list of divisors).
First departs from A137428 at a(11) = 72.
LINKS
EXAMPLE
72 is in the sequence. The divisors of 72 are {1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72} and their corresponding derivatives are {0, 1, 1, 4, 5, 12, 6, 16, 21, 44, 60, 156}. Since 8 < 9, and 8' = 12 > 6 = 9', 72 is a member.
MATHEMATICA
ad[1] = 0; ad[n_] := n * Plus @@ ((Last[#]/First[#]) & /@ FactorInteger[n]); q[n_] := Module[{d = Divisors[n]}, AnyTrue[Range[Length[d] - 1], ad[d[[#]]] > ad[d[[# + 1]]] &]]; Select[Range[200], q] (* Amiram Eldar, Nov 25 2023 *)
CROSSREFS
Cf. A003415 (n'), A137428.
Sequence in context: A269986 A139805 A141823 * A137428 A368089 A367455
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Nov 24 2023
STATUS
approved

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Last modified March 5 09:09 EST 2024. Contains 370545 sequences. (Running on oeis4.)