A240529 - OEIS

%I #27 Sep 08 2022 08:46:07

%S 224,351,624,704,735,768,783,800,832,864,895,944,959,960,999,1151,

%T 1152,1224,1279,1343,1344,1375,1440,1520,1539,1824,1855,1935,1943,

%U 1944,1952,2000,2144,2159,2176,2187,2295,2367,2430,2432,2464,2495,2496,2499,2511

%N Indices of 9-almost prime triangular numbers.

%H Vincenzo Librandi, <a href="/A240529/b240529.txt">Table of n, a(n) for n = 1..1000</a>

%F { m :  A069904(m) = 9 }. - _Alois P. Heinz_, Aug 05 2019

%e a(1) = 224 because A000217(224) = 224*(224+1)/2 = 25200 = 2^4 * 3^2 * 5^2 * 7 is a 9-almost prime.

%t Flatten[Position[Accumulate[Range[3500]], _?(PrimeOmega[#]== 9 &)]]

%t Select[Range[3000], PrimeOmega[(# (# + 1))/2] == 9 &] (* _Harvey P. Dale_, Jun 22 2017 *)

%o (Magma) [n: n in [2..2600] | &+[d[2]: d in Factorization((n*(n+1)))] eq 10]; // _Vincenzo Librandi_, Dec 22 2018

%o (GAP) F:=List([1..2600],n->Length(Factors(n*(n+1)/2)));; a:=Filtered([1..Length(F)],i->F[i]=9); # _Muniru A Asiru_, Dec 22 2018

%Y Cf. A000217, A069904, A108815, A114435, A114436, A114437, A164977.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Apr 07 2014