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
CROSSREFS
KEYWORD
AUTHOR
STATUS
approved