A299756 Triangle read by rows in which row n is the finite increasing sequence, or set of positive integers, with FDH number n.

1, 2, 3, 4, 1, 2, 5, 1, 3, 6, 1, 4, 7, 2, 3, 8, 1, 5, 2, 4, 9, 10, 1, 6, 11, 3, 4, 2, 5, 1, 7, 12, 1, 2, 3, 13, 1, 8, 2, 6, 3, 5, 14, 1, 2, 4, 15, 1, 9, 2, 7, 1, 10, 4, 5, 3, 6, 16, 1, 11, 2, 8, 1, 3, 4, 17, 1, 2, 5, 18, 3, 7, 4, 6, 1, 12, 19, 2, 9, 20, 1, 13

Offset

1,2

Comments

Let f(n) = A050376(n) be the n-th number of the form p^(2^k) where p is prime and k >= 0. The FDH number of a set S is Product_{x in S} f(x).

Same as A299755 with rows reversed.

Links

Table of n, a(n) for n=1..82.

Example

Sequence of sets begins: {}, {1}, {2}, {3}, {4}, {1,2}, {5}, {1,3}, {6}, {1,4}, {7}, {2,3}, {8}, {1,5}, {2,4}, {9}, {10}, {1,6}, {11}, {3,4}, {2,5}, {1,7}, {12}, {1,2,3}, {13}.

Mathematica

FDfactor[n_]:=If[n===1, {}, Sort[Join@@Cases[FactorInteger[n], {p_, k_}:>Power[p, Cases[Position[IntegerDigits[k, 2]//Reverse, 1], {m_}->2^(m-1)]]]]];
nn=200; FDprimeList=Array[FDfactor, nn, 1, Union];
FDrules=MapIndexed[(#1->#2[[1]])&, FDprimeList];
Join@@Table[FDfactor[n]/.FDrules, {n, 60}]

Crossrefs

Row lengths are A064547.

Cf. A005117, A050376, A112798, A213925, A246867, A277098, A296150, A299090, A299755, A299757, A299759.

Sequence in context: A024855 A274651 A074057 * A163258 A357143 A337210

Adjacent sequences: A299753 A299754 A299755 * A299757 A299758 A299759

Keyword

nonn,tabf

Author

Gus Wiseman, Feb 18 2018

Status

approved