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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 Table of n, a(n) for n=1..56. 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 Adjacent sequences: A367629 A367630 A367631 * A367633 A367634 A367635 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.)