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Smallest triangular number with n prime factors (counted with multiplicity).
10

%I #18 Feb 14 2015 21:07:02

%S 1,3,6,28,36,120,528,2080,2016,25200,32640,819840,131328,7874496,

%T 20476800,52433920,8386560,102767616,536887296,2147450880,26306560000,

%U 16240435200,116802736128,34359607296,2199022206976,549755289600

%N Smallest triangular number with n prime factors (counted with multiplicity).

%H Donovan Johnson, <a href="/A075088/b075088.txt">Table of n, a(n) for n = 0..51</a>

%e a(3)=28 because 28 is a triangular number with 3 prime factors: 28 = 2*2*7.

%o (PARI) a(n)=if(n<0,0,s=1; while(abs(bigomega(s*(s+1)/2)-n)>0,s++); s*(s+1)/2)

%Y Cf. A000217, A076550.

%K nonn

%O 0,2

%A _Amarnath Murthy_, Sep 13 2002

%E More terms from _Benoit Cloitre_, Sep 17 2002

%E a(21)-a(24) from Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 15 2004

%E Edited by _Ray Chandler_, Dec 17 2004

%E a(25) from _Ray Chandler_, Dec 22 2004