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 A307964 Irregular triangle read by rows: T(n,k) = A308121(A024556(n),k). 1
 7, 14, 13, 4, 11, 2, 1, 8, 3, 6, 5, 8, 3, 2, 5, 4, -1, 2, 1, 4, 13, 26, 19, 32, 25, 38, 31, 4, 17, 10, 23, 16, 29, 2, -5, 8, 1, 14, 7, 20, 11, 22, 33, 44, 31, 18, 29, 16, 27, 38, 1, 12, 23, 34, -3, 8, 19, 6, 17, 4, -9, 2, 13, 24, 5, 10, 7, 12, 9, 14, 11, 16, 5 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The sequence gives odd squarefree composite rows n in A308121, i.e., rows 15, 21, 33, 35, 39, 51, 55, 57, 65, ... given by A024556(n). These rows are the primitive rows of A308121. Row n has length A000010(A024556(n)). For row n: T(n, 1) = T(n, 2) / 2. T(n, phi(n)) - T(n, phi(n)-1) = T(n, 1). T(n, phi(n)/2+1) - T(n, phi(n)/2) = T(n, 1). From Charlie Neder, Jul 30 2019: (Start) For row n, T(n, k) + T(n, phi(n)-k) is constant for all k. For 2 <= k < lpf(A024556(n)), T(n, k) = k*T(n, 1). (End) LINKS Jamie Morken, Table of n, a(n) for n = 1..9768 EXAMPLE The sequence as an irregular triangle: 1: 7, 14, 13, 4, 11, 2, 1, 8; 2: 3, 6, 5, 8, 3, 2, 5, 4, -1, 2, 1, 4; 3: 13, 26, 19, 32, 25, 38, 31, 4, 17, 10, 23, 16, 29, 2, -5, 8, 1, 14, 7, 20; 4: 11, 22, 33, 44, 31, 18, 29, 16, 27, 38, 1, 12, 23, 34, -3, 8, 19, 6, 17, 4, -9, 2, 13, 24; 5: 5, 10, 7, 12, 9, 14, 11, 16, 5, 2, 7, 4, 9, 6, 11, 8, -3, 2, -1, 4, 1, 6, 3, 8 6: 19, 38, 25, 44, 31, 50, 37, 56, 43, 62, 49, 4, 23, 10, 29, 16, 35, 22, 41, 28, 47, 2, -11, 8, -5, 14, 1, 20, 7, 26, 13, 32; 7: 3, 6, 9, 12, 7, 10, 13, 16, 3, 6, 9, 4, 7, 10, 13, 8, 3, 6, 1, 4, 7, 10, 5, 8, 3, -2, 1, 4, 7, 2, 5, 8, -5, -2, 1, 4, -1, 2, 5, 8; 8: 7, 14, 9, 16, 11, 18, 13, 20, 15, 22, 17, 24, 7, 2, 9, 4, 11, 6, 13, 8, 15, 10, 17, 12, -5, 2, -3, 4, -1, 6, 1, 8, 3, 10, 5, 12; 9: 17, 34, 51, 68, 37, 54, 71, 88, 57, 74, 43, 12, 29, 46, 63, 32, 49, 66, 83, 4, 21, 38, 7, 24, 41, 58, 27, 44, 61, -18, -1, 16, 33, 2, 19, 36, 53, 22, -9, 8, -23, -6, 11, 28, -3, 14, 31, 48; ... MATHEMATICA rowsToCheck = 340; A024556 = Complement[Select[Range[3, rowsToCheck, 2], SquareFreeQ], Prime[Range[ PrimePi[rowsToCheck]]]]; (* after Harvey P. Dale , Jan 26 2011 *) A308121 = Table[With[{a = n/GCD[n, #], b = Numerator[#/n]}, MapIndexed[a First@#2 - b #1 &, Flatten@Position[GCD[Table[Mod[k, n], {k, n - 1}], n], 1] /. {} -> {1}]] &@EulerPhi@n, {n, rowsToCheck}]; (* after Michael De Vlieger, Jun 06 2019 *) A307964 = {}; For[i = 1, i <= Length[A024556], i++, AppendTo[A307964, A308121[[A024556[[i]]]]]] A307964flattened = Flatten[A307964] (* Jamie Morken, Apr 20 2021 *) CROSSREFS Cf. A024556, A308121, A309497, A000010, A076511, A076512. Sequence in context: A295123 A196178 A269161 * A225556 A064666 A269160 Adjacent sequences: A307961 A307962 A307963 * A307965 A307966 A307967 KEYWORD sign,look,tabf AUTHOR Jamie Morken, Jul 29 2019 STATUS approved

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Last modified August 5 17:52 EDT 2024. Contains 374954 sequences. (Running on oeis4.)