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 A189553 Irregular triangle in which row n contains numbers x such that x'=n, where x' denotes the arithmetic derivative (A003415). 3
 4, 6, 9, 10, 15, 14, 21, 25, 8, 35, 22, 33, 49, 26, 12, 39, 55, 65, 77, 34, 51, 91, 18, 38, 57, 85, 121, 20, 95, 119, 143, 46, 69, 133, 169, 27, 115, 187, 161, 209, 221, 30, 58, 16, 28, 87, 247, 62, 93, 145, 253, 289, 155, 203, 299, 323, 217, 361, 45, 74 (list; graph; refs; listen; history; text; internal format)
 OFFSET 4,1 COMMENTS Row 0 contains 0 and 1. Row 1 contains all primes. Rows 2 and 3 are empty. Hence, we start this table with row 4. The length of row n is A099302(n). The first term in row n is A098699(n). The last term is A099303(n). Row n is the set I(n) in the paper by Ufnarovski and Ahlander. They show that all terms in row n are <= (n/2)^2. The upper bound is attained when n = 2p, where p is a prime. REFERENCES See A003415. LINKS T. D. Noe, Rows n = 4..1000, flattened Victor Ufnarovski and Bo Ahlander, How to Differentiate a Number, J. Integer Seqs., Vol. 6, 2003. EXAMPLE The triangle begins 4 6 9 10 15 14 21, 25 none 8, 35 22 33, 49 26 12, 39, 55 MATHEMATICA dn = 0; dn = 0; dn[n_] := Module[{f = Transpose[FactorInteger[n]]}, If[PrimeQ[n], 1, Plus @@ (n*f[]/f[])]]; nn = 100; d = Array[dn, (nn/2)^2]; Table[Flatten[Position[d, n]], {n, 4, nn}] CROSSREFS Cf. A003415, A098699, A099302, A099303. Sequence in context: A132435 A108631 A200677 * A189482 A099303 A243485 Adjacent sequences:  A189550 A189551 A189552 * A189554 A189555 A189556 KEYWORD nonn,tabf AUTHOR T. D. Noe, Apr 23 2011 STATUS approved

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Last modified September 27 19:34 EDT 2021. Contains 347694 sequences. (Running on oeis4.)