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A261144 Irregular triangle of numbers that are squarefree and smooth (row n contains squarefree p-smooth numbers, where p is the n-th prime). 3
1, 2, 1, 2, 3, 6, 1, 2, 3, 5, 6, 10, 15, 30, 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210, 1, 2, 3, 5, 6, 7, 10, 11, 14, 15, 21, 22, 30, 33, 35, 42, 55, 66, 70, 77, 105, 110, 154, 165, 210, 231, 330, 385, 462, 770, 1155, 2310, 1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 21, 22, 26, 30, 33, 35, 39, 42 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Jean-François Alcover, Table of n, a(n) for n = 1..2046 (first 10 rows)

A. Hildebrand, G. Tenenbaum, Integers without large prime factors, Journal de théorie des nombres de Bordeaux (1993) Volume:5, Issue:2, p. 411-484.

Eric Weisstein's MathWorld, Smooth number.

Wikipedia, Smooth number

EXAMPLE

Triangle begins:

1, 2;                        squarefree and 2-smooth

1, 2, 3, 6;                  squarefree and 3-smooth

1, 2, 3, 5, 6, 10, 15, 30;

1, 2, 3, 5, 6,  7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210;

...

MAPLE

b:= proc(n) option remember; `if`(n=0, [1],

      sort(map(x-> [x, x*ithprime(n)][], b(n-1))))

    end:

T:= n-> b(n)[]:

seq(T(n), n=1..7);  # Alois P. Heinz, Nov 28 2015

MATHEMATICA

primorial[n_] := Times @@ Prime[Range[n]]; row[n_] := Select[ Divisors[ primorial[n]], SquareFreeQ]; Table[row[n], {n, 1, 10}] // Flatten

CROSSREFS

Cf. A000079 (2-smooth), A003586 (3-smooth), A051037 (5-smooth), A002473 (7-smooth), A018336 (7-smooth & squarefree), A051038 (11-smooth), A087005 (11-smooth & squarefree), A080197 (13-smooth), A087006 (13-smooth & squarefree), A087007 (17-smooth & squarefree), A087008 (19-smooth & squarefree).

Sequence in context: A079210 A070861 A277566 * A106524 A323641 A086582

Adjacent sequences:  A261141 A261142 A261143 * A261145 A261146 A261147

KEYWORD

nonn,tabf

AUTHOR

Jean-François Alcover, Nov 26 2015

STATUS

approved

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Last modified November 22 03:20 EST 2019. Contains 329383 sequences. (Running on oeis4.)