

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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

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



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]]
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 *)


CROSSREFS



KEYWORD

fini,more,nonn


AUTHOR



EXTENSIONS



STATUS

approved



