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 A372323 A124652(n) is the a(n)-th term in row A372111(n-1) of irregular triangle A162306. 2
 2, 4, 4, 4, 5, 7, 5, 8, 8, 2, 10, 8, 12, 11, 13, 6, 13, 6, 6, 9, 8, 11, 4, 8, 16, 5, 6, 7, 13, 12, 7, 10, 19, 15, 16, 17, 9, 6, 15, 10, 3, 11, 8, 18, 28, 14, 14, 10, 30, 28, 15, 4, 20, 33, 13, 12, 6, 22, 18, 21, 12, 11, 29, 12, 11, 8, 24, 18, 8, 14, 17, 32, 33 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,1 COMMENTS Let b(x) = A124652(x) and let s(x) = A372111(x), where A372111 contains partial sums of A124652. Let r(x) = A010846(x), the number of m <= x such that rad(m) | x, where rad = A007947. Let row k of A162306 contain { m : rad(m) | k, m <= k }. Thus r(k) is the length of row k of A162306. Let T(k,j) represent the j-th term in row k of irregular triangle A162306. a(n) = j is the position of b(n) in row s(n-1) of A162306. b(n) = T(s(n-1), a(n)). Analogous to A371910, which instead regards A109890 and A109735. LINKS Michael De Vlieger, Table of n, a(n) for n = 3..10000 Michael De Vlieger, Bar chart showing a(n)/A372322(n-1) for n = 3..1024. This chart illustrates the "depth" of A124652(n) among the terms of the A372111(n-1)-th row of A162306. EXAMPLE Let b(x) = A124652(x) and let s(x) = A372111(x), where A372111 contains partial sums of A124652. a(3) = 2 since b(3) = 3 is the 2nd term in row s(3) = 3 of A162306, {1, [3]}. a(4) = 4 since b(4) = 4 is the 4th term in row s(4) = 6 of A162306, {1, 2, 3, [4], 6}. a(5) = 4 since b(5) = 5 is T(s(n-1), 4) = T(10, 4), {1, 2, 4, [5], 8, 10}. a(6) = 4 since b(6) = 9 is T(s(n-1), 4) = T(15, 4), {1, 3, 5, [9], 15}. a(7) = 5 since b(7) = 6 is T(s(n-1), 5) = T(24, 5), {1, 2, 3, 4, [6], 8, 9, 12, 16, 18, 24}, etc. Table relating this sequence to b = A124652, s = A372111, r = A372322, and A162306. n b(n) s(n-1) a(n) r(n) row s(n-1) of A162306 --------------------------------------------------------------------- 3 3 3 2 2 {1, [3]} 4 4 6 4 5 {1, 2, 3, [4], 6} 5 5 10 4 6 {1, 2, 4, [5], 8, 10} 6 9 15 4 5 {1, 3, 5, [9], 15} 7 6 24 5 11 {1, 2, 3, 4, [6], ..., 24} 8 8 30 7 18 {1, 2, 3, 4, 5, 6, [8], ..., 30} 9 16 38 5 8 {1, 2, 4, 8, [16], 19, 32, 38} 10 12 54 8 16 {1, 2, 3, 4, 6, 8, 9, [12], ..., 54} 11 11 66 8 22 {1, 2, 3, 4, 6, 8, 9, [11], ..., 66} 12 7 77 2 5 {1, [7], 11, 49, 77} 13 14 84 10 28 {1, 2, 3, 4, ..., 12, [14], ..., 84} 14 28 98 8 13 {1, 2, 4, 7, ..., 16, [28], ..., 98} MATHEMATICA nn = 75; c[_] := False; rad[x_] := rad[x] = Times @@ FactorInteger[x][[All, 1]]; f[x_] := Select[Range[x], Divisible[x, rad[#]] &]; Array[Set[{a[#], c[#]}, {#, True}] &, 2]; s = a[1] + a[2]; Reap[Do[r = f[s]; k = SelectFirst[r, ! c[#] &]; Sow[FirstPosition[r, k][[1]]]; c[k] = True; s += k, {i, 3, nn}] ][[-1, 1]] CROSSREFS Cf. A007947, A010846, A124652, A162306, A371910, A372111, A372322. Sequence in context: A132345 A178976 A352426 * A130766 A227190 A284581 Adjacent sequences: A372320 A372321 A372322 * A372324 A372325 A372326 KEYWORD nonn AUTHOR Michael De Vlieger, May 05 2024 STATUS approved

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Last modified July 21 09:16 EDT 2024. Contains 374472 sequences. (Running on oeis4.)