A372514 Index k such that A280864(k) = A019565(n) or 0 if A019565(n) does not appear in A280864.
1, 2, 4, 5, 7, 8, 17, 26, 11, 12, 20, 37, 36, 72, 73, 207, 14, 15, 43, 68, 42, 106, 107, 310, 47, 151, 152, 442, 294, 745, 746, 2227, 23, 22, 44, 53, 52, 130, 114, 386, 83, 188, 156, 519, 189, 884, 754, 2573, 115, 269, 270, 816, 387, 1405, 1406, 4134, 563, 1954
Offset: 0
Keywords
Examples
Let s = A019565 and let t = A280864. a(0) = 1 since s(0) = 1 = t(1). a(1) = 2 since s(1) = 2 = t(2). a(2) = 4 since s(2) = 3 = t(4). a(3) = 5 since s(3) = 5 = t(5). Table relating this sequence to s and t. The last column shows Y if s(n) is divisible by the prime in the heading, otherwise ".": n s(n) a(n) 2357 ---------------------- 0 1 1 . 1 2 2 Y 2 3 4 .Y 3 6 5 YY 4 5 7 ..Y 5 10 8 Y.Y 6 15 17 .YY 7 30 26 YYY 8 7 11 ...Y 9 14 12 Y..Y 10 21 20 .Y.Y 11 42 37 YY.Y 12 35 36 .YYY 13 70 72 Y.YY 14 105 73 .YYY 15 210 207 YYYY ...
Links
- Michael De Vlieger, Table of n, a(n) for n = 0..478
- Michael De Vlieger, Fan style binary tree showing a(n), n = 0..2047, with a color code associated with log(a(n))/log(2) for a(n) <= 262144. Terms that are either 0 or greater than 262144 appear blank.
Programs
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Mathematica
nn = 2^13; r = s = 1; c[_] := False; rad[n_] := rad[n] = Times @@ FactorInteger[n][[All, 1]]; a = Monitor[Reap[Do[w = GCD[r, s]; k = m = r/w; While[Or[c[k], ! CoprimeQ[w, k] ], k += m]; Sow[k]; c[k] = True; s = r; r = rad[k], {i, nn}]][[-1, 1]], i]; Array[FirstPosition[a, Times @@ Prime@ Position[Reverse[IntegerDigits[#, 2]], 1][[All, 1]] ][[1]] &, 61, 0]
Formula
a(2^k) > 0 and a(2*m+1) > 0, consequences of Theorem 1 in A280864.
Comments