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A299756 Triangle read by rows in which row n is the finite increasing sequence, or set of positive integers, with FDH number n. 7
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 (list; graph; refs; listen; history; text; internal format)
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 A141063 A138223

Adjacent sequences:  A299753 A299754 A299755 * A299757 A299758 A299759

KEYWORD

nonn,tabf

AUTHOR

Gus Wiseman, Feb 18 2018

STATUS

approved

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Last modified October 15 17:24 EDT 2019. Contains 328037 sequences. (Running on oeis4.)