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 A067820 #33 Aug 31 2025 12:55:25
%S A067820 32,944,15470,57967,632148,14845324,69921004,888781058,2674685524,
%T A067820 10077383364,21117216104,393370860205,3157222675953,5509463413255,
%U A067820 24819420480104,361385490681003,441826936079342
%N A067820 The start of a record-breaking run of consecutive integers with a number of prime factors (counted with multiplicity) equal to 5.
%C A067820 a(16) > 3*10^13. - _Brian Trial_, May 13 2017
%C A067820 All multiples of 32 greater than 32 are of form 2^5*m and have at least 6 factors. Thus this sequence will be limited to a run of at most 31 integers. - _Brian Trial_, May 13 2017
%C A067820 a(18) > 2 * 10^15. - _Toshitaka Suzuki_, Aug 31 2025
%e A067820 a(3)=15470 because 15470 is the start of a record breaking run of 3 consecutive integers (15470 to 15472) each having 5 prime factors; i.e. bigomega(n)=A001222(n)=5 for n = 15470, ..., 15472.
%t A067820 bigomega[n_] := Plus@@Last/@FactorInteger[n]; For[n=1; m=l=0, True, n++, If[bigomega[n]==5, l++, If[l>m, m=l; Print[n-l, " ", l]]; l=0]]
%t A067820 Table[SequencePosition[PrimeOmega[Range[15*10^6]],PadRight[{},n,5],1][[All,1]],{n,6}]//Flatten (* The program generates the first six terms of the sequence. *) (* _Harvey P. Dale_, Sep 03 2022 *)
%Y A067820 Cf. A067813, A067814, A067821, A067822.
%Y A067820 Subsequence of A014614.
%K A067820 fini,more,nonn,changed
%O A067820 1,1
%A A067820 _Shyam Sunder Gupta_, Feb 07 2002
%E A067820 Edited by _Dean Hickerson_, Jul 31 2002
%E A067820 More terms from _Jens Kruse Andersen_, Aug 23 2003
%E A067820 a(13)-a(14) from _Donovan Johnson_, Jan 31 2009
%E A067820 a(15) from _Brian Trial_, May 13 2017
%E A067820 a(16)-a(17) from _Toshitaka Suzuki_, Aug 31 2025