This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A101744 #12 Feb 16 2025 08:32:55
%S A101744 32640,73920,130816,165600,204480,265356,294528,401856,592416,839160,
%T A101744 947376,990528,1279200,1445850,1492128,1606528,1842240,1844160,
%U A101744 2031120,2049300,2821500,2956096,3571128,3963520,4148640,4250070,4335040
%N A101744 Triangular numbers which are 10-almost primes.
%C A101744 A101745 contains the indices of this sequence, i.e. T(n) for what values of n are these 10-almost primes.
%D A101744 Ball, W. W. R. and Coxeter, H. S. M. Mathematical Recreations and Essays, 13th ed. New York: Dover, p. 59, 1987.
%D A101744 Conway, J. H. and Guy, R. K. The Book of Numbers. New York: Springer-Verlag, pp. 33-38, 1996.
%D A101744 Dudeney, H. E. Amusements in Mathematics. New York: Dover, pp. 67 and 167, 1970.
%H A101744 Charles R Greathouse IV, <a href="/A101744/b101744.txt">Table of n, a(n) for n = 1..10000</a>
%H A101744 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TriangularNumber.html">Triangular Number</a>.
%H A101744 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AlmostPrime.html">Almost Prime</a>.
%F A101744 a(n) is in the intersection of {A000217} and {A046314}. Integers of the form k*(k+1)/2 which have exactly 10 prime factors.
%e A101744 a(1) = 32640 because that is the smallest triangular number which is also a 10-almost prime; specifically T(255) = 255*(255+1)/2 = 32640 = 2^7 * 3 * 5 * 17.
%t A101744 BigOmega[n_Integer]:=Plus@@Last[Transpose[FactorInteger[n]]]; Select[Table[n*(n+1)/2, {n, 2, 5000}], BigOmega[ # ]==10&] (* _Ray Chandler_, Dec 14 2004 *)
%o A101744 (PARI) list(lim)=my(v=List(),cur,last=3,n=256,t); while((t=n*(n-1)/2) <= lim, cur=bigomega(n); if(cur+old==11, listput(v,t)); old=cur; n++); Vec(v) \\ _Charles R Greathouse IV_, Feb 05 2017
%Y A101744 Cf. A000217, A046314, A068443, A075875, A076578-A076583, A075088, A101745.
%K A101744 easy,nonn
%O A101744 1,1
%A A101744 _Jonathan Vos Post_, Dec 14 2004
%E A101744 More terms from _Ray Chandler_, Dec 14 2004