A067821 - OEIS

%I #32 Aug 31 2025 12:55:17

%S 64,5264,33614,8706123,101905622,4843161124,25189114374,412352139170,

%T 1122875553872,28099912628847,78661670985666

%N The start of a record-breaking run of consecutive integers with a number of prime factors (counted with multiplicity) equal to 6.

%C a(11) > 3*10^13. - _Brian Trial_, May 26 2017

%C a(12) > 2 * 10^15. - _Toshitaka Suzuki_, Aug 31 2025

%e a(3)=33614 because 33614 is the start of a record breaking run of 3 consecutive integers (33614 to 33616) each having 6 prime factors; i.e., bigomega(n)=A001222(n)=6 for n = 33614, ..., 33616.

%t bigomega[n_] := Plus@@Last/@FactorInteger[n]; For[n=1; m=l=0, True, n++, If[bigomega[n]==6, l++, If[l>m, m=l; Print[n-l, " ", l]]; l=0]]

%Y Cf. A001222, A067813, A067814, A067820, A067822.

%K fini,more,nonn

%O 1,1

%A _Shyam Sunder Gupta_, Feb 07 2002

%E Edited by _Dean Hickerson_, Jul 31 2002

%E More terms from _Jens Kruse Andersen_, Aug 23 2003

%E a(7)-a(9) from _Donovan Johnson_, Jan 31 2009

%E a(10) from _Brian Trial_, May 26 2017

%E a(11) from _Toshitaka Suzuki_, Aug 31 2025