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 A058812 Irregular triangle of rows of numbers in increasing order. Row 1 = {1}. Row m + 1 contains all numbers k such that phi(k) is in row m. 8
 1, 2, 3, 4, 6, 5, 7, 8, 9, 10, 12, 14, 18, 11, 13, 15, 16, 19, 20, 21, 22, 24, 26, 27, 28, 30, 36, 38, 42, 54, 17, 23, 25, 29, 31, 32, 33, 34, 35, 37, 39, 40, 43, 44, 45, 46, 48, 49, 50, 52, 56, 57, 58, 60, 62, 63, 66, 70, 72, 74, 76, 78, 81, 84, 86, 90, 98, 108, 114, 126 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Nontotient values (A007617) are also present as inverses of some previous value. Old name was: Irregular triangle of inverse totient values of integers generated recursively. Initial value is 1. The inverse-phi sets in increasing order are as follows: {1} -> {2} -> {3, 4, 6} -> {5, 7, 8, 9, 10, 12, 14, 18} -> ... The terms of each row are arranged by magnitude. The next row starts when the increase of terms is violated. 2^n is included in the n-th row. - David A. Corneth, Mar 26 2019 LINKS T. D. Noe, Rows n=0..9 of triangle, flattened Hartosh Singh Bal, Gaurav Bhatnagar, Prime number conjectures from the Shapiro class structure, arXiv:1903.09619 [math.NT], 2019. T. D. Noe, Primes in classes of the iterated totient function, JIS 11 (2008) 08.1.2. EXAMPLE Triangle begins:   1;   2;   3, 4, 6;   5, 7, 8, 9, 10, 12, 14, 18;   ... Row 3 is {3, 4, 6} as for each number k in this row, phi(k) is in row 2. - David A. Corneth, Mar 26 2019 MATHEMATICA inversePhi[m_?OddQ] = {}; inversePhi[1] = {1, 2}; inversePhi[m_] := Module[{p, nmax, n, nn}, p = Select[Divisors[m] + 1, PrimeQ]; nmax = m*Times @@ (p/(p-1)); n = m; nn = {}; While[n <= nmax, If[EulerPhi[n] == m, AppendTo[nn, n]]; n++]; nn]; row[n_] := row[n] = inversePhi /@ row[n-1] // Flatten // Union; row[0] = {1}; row[1] = {2}; Table[row[n], {n, 0, 5}] // Flatten (* Jean-François Alcover, Dec 06 2012 *) CROSSREFS Cf. A000010, A007617, A005277. A058811 gives the number of terms in each row. Cf. A003434, A007755, A060611, A092878, A098196, A135832. Cf. also A334111. Sequence in context: A129607 A130340 A130339 * A320454 A320455 A072796 Adjacent sequences:  A058809 A058810 A058811 * A058813 A058814 A058815 KEYWORD nonn,tabf,nice,look AUTHOR Labos Elemer, Jan 03 2001 EXTENSIONS Definition revised by T. D. Noe, Nov 30 2007 New name from David A. Corneth, Mar 26 2019 STATUS approved

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Last modified July 30 19:33 EDT 2021. Contains 346359 sequences. (Running on oeis4.)