A067821 The start of a record-breaking run of consecutive integers with a number of prime factors (counted with multiplicity) equal to 6.

64, 5264, 33614, 8706123, 101905622, 4843161124, 25189114374, 412352139170, 1122875553872, 28099912628847, 78661670985666

Offset: 1

Author

Shyam Sunder Gupta, Feb 07 2002

Keywords

• fini
• more
• nonn
• changed

Comments

a(11) > 3*10^13. - Brian Trial, May 26 2017

a(12) > 2 * 10^15. - Toshitaka Suzuki, Aug 31 2025

Examples

			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.
		

Crossrefs

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

Programs

Mathematica

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]]

Extensions

Edited by Dean Hickerson, Jul 31 2002

More terms from Jens Kruse Andersen, Aug 23 2003

a(7)-a(9) from Donovan Johnson, Jan 31 2009

a(10) from Brian Trial, May 26 2017

a(11) from Toshitaka Suzuki, Aug 31 2025