A067820 The start of a record-breaking run of consecutive integers with a number of prime factors (counted with multiplicity) equal to 5.

32, 944, 15470, 57967, 632148, 14845324, 69921004, 888781058, 2674685524, 10077383364, 21117216104, 393370860205, 3157222675953, 5509463413255, 24819420480104, 361385490681003, 441826936079342

Offset: 1

Author

Shyam Sunder Gupta, Feb 07 2002

Keywords

• fini
• more
• nonn
• changed

Comments

a(16) > 3*10^13. - Brian Trial, May 13 2017

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

a(18) > 2 * 10^15. - Toshitaka Suzuki, Aug 31 2025

Examples

			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.
		

Crossrefs

Cf. A067813, A067814, A067821, A067822.

Subsequence of A014614.

Programs

Mathematica

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]]
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 *)

Extensions

Edited by Dean Hickerson, Jul 31 2002

More terms from Jens Kruse Andersen, Aug 23 2003

a(13)-a(14) from Donovan Johnson, Jan 31 2009

a(15) from Brian Trial, May 13 2017

a(16)-a(17) from Toshitaka Suzuki, Aug 31 2025