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 A365901 Irregular triangle read by rows giving trajectory beginning with A002182(n) under recursion of x -> f(x) until reaching 1, where f(x) = x/rad(x), rad(x) = A007947(x). 1
 1, 2, 1, 4, 2, 1, 6, 1, 12, 2, 1, 24, 4, 2, 1, 36, 6, 1, 48, 8, 4, 2, 1, 60, 2, 1, 120, 4, 2, 1, 180, 6, 1, 240, 8, 4, 2, 1, 360, 12, 2, 1, 720, 24, 4, 2, 1, 840, 4, 2, 1, 1260, 6, 1, 1680, 8, 4, 2, 1, 2520, 12, 2, 1, 5040, 24, 4, 2, 1, 7560, 36, 6, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Let h(n) = A002182(n). Since highly composite numbers h(n) are products of primorials (i.e., in A025487), the squarefree kernel is always a primorial (i.e., in A002110), and the trajectory always reaches 1. LINKS Michael De Vlieger, Table of n, a(n) for n = 1..11397 (rows n = 1..1200, flattened) Michael De Vlieger, Log log scatterplot of log_10(a(n)), n = 1..1053678, showing 2^16 rows. FORMULA Length of row n is A112779(n)+1. T(n,2) = A301413(n), n > 1. EXAMPLE Row 1 = {1} since h(1) = 1, already 1. Row 2 = {2, 1} since h(2) = 2, 2/rad(2) = 2/2 = 1, reaching 1. Row 3 = {4, 2, 1} since h(3) = 4, 4/rad(4) = 4/2 = 2, and we follow the trajectory of 2 thereafter. Row 6 = {24, 4, 2, 1} since h(6) = 24, 24/rad(24) = 24/6 = 4, and we follow the trajectory of 4 thereafter. Row 14 = {720, 24, 4, 2, 1} since h(14) = 720, 720/rad(720) = 720/30 = 24, which appends row 6 thereafter. . First rows of this sequence: row 1: 1 2: 2, 1 3: 4, 2, 1 4: 6, 1 5: 12, 2, 1 6: 24, 4, 2, 1 7: 36, 6, 1 8: 48, 8, 4, 2, 1 9: 60, 2, 1 10: 120, 4, 2, 1 11: 180, 6, 1 12: 240, 8, 4, 2, 1 ... MATHEMATICA a2182 = Import["https://oeis.org/A002182/b002182.txt", "Data"][[All, -1]]; Array[NestWhileList[#/(Times @@ FactorInteger[#][[All, 1]]) &, a2182[[#]], # > 1 &] &, 20] // TableForm CROSSREFS Cf. A002110, A002182, A007947, A112779, A301413, A365900. Sequence in context: A329504 A147542 A347069 * A325309 A211956 A128177 Adjacent sequences: A365898 A365899 A365900 * A365902 A365903 A365904 KEYWORD nonn,tabf AUTHOR Michael De Vlieger, Oct 11 2023 STATUS approved

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Last modified July 21 18:08 EDT 2024. Contains 374475 sequences. (Running on oeis4.)