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 A334111 Irregular triangle where row n gives all terms k for which A064097(k) = n. 9
 1, 2, 3, 4, 5, 6, 8, 7, 9, 10, 12, 16, 11, 13, 14, 15, 17, 18, 20, 24, 32, 19, 21, 22, 25, 26, 27, 28, 30, 34, 36, 40, 48, 64, 23, 29, 31, 33, 35, 37, 38, 39, 41, 42, 44, 45, 50, 51, 52, 54, 56, 60, 68, 72, 80, 96, 128, 43, 46, 49, 53, 55, 57, 58, 61, 62, 63, 65, 66, 70, 73, 74, 75, 76, 78, 81, 82, 84 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Applying map k -> (p-1)*(k/p) to any term k on any row n > 1, where p is any prime factor of k, gives one of the terms on preceding row n-1. Any prime that appears on row n is 1 + {some term on row n-1}. The e-th powers of the terms on row n form a subset of terms on row (e*n). More generally, a product of terms that occur on rows i_1, i_2, ..., i_k can be found at row (i_1 + i_2 + ... + i_k), because A064097 is completely additive. A001221(k) gives the number of terms on the row above that are immediate descendants of k. A067513(k) gives the number of terms on the row below that lead to k. LINKS Michael De Vlieger, Table of n, a(n) for n = 0..14422 (rows 0 <= n <= 17, flattened) EXAMPLE Rows 0-6 of the irregular table: 0 |   1; 1 |   2; 2 |   3, 4; 3 |   5, 6, 8; 4 |   7, 9, 10, 12, 16; 5 |  11, 13, 14, 15, 17, 18, 20, 24, 32; 6 |  19, 21, 22, 25, 26, 27, 28, 30, 34, 36, 40, 48, 64; MATHEMATICA f[n_] := Length@ NestWhileList[# - #/FactorInteger[#][[1, 1]] &, n, # != 1 &]; SortBy[ Range@70, f] (* Second program *) With[{nn = 8}, Values@ Take[KeySort@ PositionIndex@ Array[-1 + Length@ NestWhileList[# - #/FactorInteger[#][[1, 1]] &, #, # > 1 &] &, 2^nn], nn + 1]] // Flatten (* Michael De Vlieger, Apr 18 2020 *) PROG (PARI) A060681(n) = (n-if(1==n, n, n/vecmin(factor(n)[, 1]))); A064097(n) = if(1==n, 0, 1+A064097(A060681(n))); for(n=0, 10, for(k=1, 2^n, if(A064097(k)==n, print1(k, ", ")))); CROSSREFS Cf. A001221, A064097, A067513, A333123, A334144. Cf. A105017 (left edge), A000079 (right edge), A175125 (row lengths). Cf. also A058812, A334100. Sequence in context: A332073 A117332 A242704 * A243571 A215366 A333483 Adjacent sequences:  A334108 A334109 A334110 * A334112 A334113 A334114 KEYWORD nonn,look,tabf AUTHOR Antti Karttunen, Michael De Vlieger and Robert G. Wilson v, Apr 14 2020 STATUS approved

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Last modified September 27 19:23 EDT 2021. Contains 347694 sequences. (Running on oeis4.)