

A067820


The start of a recordbreaking run of consecutive integers with a number of prime factors (counted with multiplicity) equal to 5.


7



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

1,1


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


LINKS

Table of n, a(n) for n=1..15.


EXAMPLE

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.


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[nl, " ", l]]; l=0]]


CROSSREFS

Cf. A067813, A067814, A067821, A067822.
Subsequence of A014614.
Sequence in context: A241223 A283412 A227441 * A263818 A220743 A115612
Adjacent sequences: A067817 A067818 A067819 * A067821 A067822 A067823


KEYWORD

fini,more,nonn


AUTHOR

Shyam Sunder Gupta, Feb 07 2002


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


STATUS

approved



