A265668 - OEIS

A265668

Table read by rows: prime factors of squarefree numbers; a(1) = 1 by convention.

1, 2, 3, 5, 2, 3, 7, 2, 5, 11, 13, 2, 7, 3, 5, 17, 19, 3, 7, 2, 11, 23, 2, 13, 29, 2, 3, 5, 31, 3, 11, 2, 17, 5, 7, 37, 2, 19, 3, 13, 41, 2, 3, 7, 43, 2, 23, 47, 3, 17, 53, 5, 11, 3, 19, 2, 29, 59, 61, 2, 31, 5, 13, 2, 3, 11, 67, 3, 23, 2, 5, 7, 71, 73, 2

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OFFSET

1,2

COMMENTS

For n > 1: A072047(n) = length of row n;

T(n,1) = A073481(n); T(n,A001221(n)) = A073482(n);

for n > 1: A111060(n) = sum of row n;

A005117(n) = product of row n.

LINKS

Reinhard Zumkeller, Rows n = 1..1000 of triangle, flattened

EXAMPLE

. n | T(n,*) A5117(n) n | T(n,*) A5117(n) n | T(n,*) A5117(n)

. ----+---------+------ ----+---------+------ ----+----------+------

. 1 | [1] | 1 21 | [3,11] | 33 41 | [2,3,11] | 66

. 2 | [2] | 2 22 | [2,17] | 34 42 | [67] | 67

. 3 | [3] | 3 23 | [5,7] | 35 43 | [3,23] | 69

. 4 | [5] | 5 24 | [37] | 37 44 | [2,5,7] | 70

. 5 | [2,3] | 6 25 | [2,19] | 38 45 | [71] | 71

. 6 | [7] | 7 26 | [3,13] | 39 46 | [73] | 73

. 7 | [2,5] | 10 27 | [41] | 41 47 | [2,37] | 74

. 8 | [11] | 11 28 | [2,3,7] | 42 48 | [7,11] | 77

. 9 | [13] | 13 29 | [43] | 43 49 | [2,3,13] | 78

. 10 | [2,7] | 14 30 | [2,23] | 46 50 | [79] | 79

. 11 | [3,5] | 15 31 | [47] | 47 51 | [2,41] | 82

. 12 | [17] | 17 32 | [3,17] | 51 52 | [83] | 83

. 13 | [19] | 19 33 | [53] | 53 53 | [5,17] | 85

. 14 | [3,7] | 21 34 | [5,11] | 55 54 | [2,43] | 86

. 15 | [2,11] | 22 35 | [3,19] | 57 55 | [3,29] | 87

. 16 | [23] | 23 36 | [2,29] | 58 56 | [89] | 89

. 17 | [2,13] | 26 37 | [59] | 59 57 | [7,13] | 91

. 18 | [29] | 29 38 | [61] | 61 58 | [3,31] | 93

. 19 | [2,3,5] | 30 39 | [2,31] | 62 59 | [2,47] | 94

. 20 | [31] | 31 40 | [5,13] | 65 60 | [5,19] | 95 .

MATHEMATICA

FactorInteger[#][[All, 1]]&/@Select[Range[100], SquareFreeQ]//Flatten (* Harvey P. Dale, Apr 27 2018 *)

PROG

(Haskell)

import Math.NumberTheory.Primes.Factorisation (factorise)

import Data.Maybe (mapMaybe)

a265668 n k = a265668_tabf !! (n-1) !! (k-1)

a265668_row n = a265668_tabf !! (n-1)

a265668_tabf = [1] : mapMaybe f [2..] where

f x = if all (== 1) es then Just ps else Nothing

where (ps, es) = unzip $ factorise x

CROSSREFS

Cf. A005117, A027748, A124010, A072047 (row lengths), A073481, A073482, A001221, A111060, A049200, A062822.

Sequence in context: A060084 A374155 A361503 * A273087 A236434 A138182

Adjacent sequences: A265665 A265666 A265667 * A265669 A265670 A265671

KEYWORD

nonn,tabf

AUTHOR

Reinhard Zumkeller, Dec 13 2015

STATUS

approved