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Triangle read by rows in which row n contains first n numbers with exactly n distinct prime factors.
9

%I #29 Jan 03 2023 14:49:59

%S 2,6,10,30,42,60,210,330,390,420,2310,2730,3570,3990,4290,30030,39270,

%T 43890,46410,51870,53130,510510,570570,690690,746130,870870,881790,

%U 903210,9699690,11741730,13123110,14804790,15825810,16546530,17160990,17687670,223092870,281291010,300690390,340510170,358888530,363993630,380570190,397687290,406816410

%N Triangle read by rows in which row n contains first n numbers with exactly n distinct prime factors.

%H David A. Corneth, <a href="/A048692/b048692.txt">Table of n, a(n) for n = 1..10011</a>

%H Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a048/A048692.java">Java program</a> (github)

%e 2;

%e 6, 10;

%e 30, 42, 60;

%e 210, 330, 390, 420;

%e ...

%t f[n_] := Flatten[Table[ # [[1]]] & /@ FactorInteger[n]]; (* for n=7 *) Take[ Select[ Range[10^7], Length[f[ # ]] == 7 & ], 7]

%t Module[{nn=8,dpf=Table[{n,PrimeNu[n]},{n,2 10^7}]},Flatten[Table[Select[dpf,#[[2]]==n&,n],{n,nn}],1][[All,1]]] (* The program generates the first 36 terms of the sequence. *) (* _Harvey P. Dale_, Sep 09 2022 *)

%Y Cf. A002110 (first column).

%Y Main diagonal gives A073329.

%Y Extending the rows to give a square array, we get A125666.

%K nonn,tabl

%O 1,1

%A _Amarnath Murthy_, Aug 20 2002

%E Edited, corrected and extended by _Robert G. Wilson v_, Aug 22 2002

%E More terms from _David A. Corneth_, Jan 09 2021