experimental-projects/oeis-research/Ilya Gutkovskiy/Consecutive integers with equal bigomega(n) - omega(n)/prog.sf

#!/usr/bin/ruby

# a(n) is the smallest number k such that factorizations of n consecutive integers starting at k have the same excess of number of primes counted with multiplicity over number of primes counted without multiplicity (A046660).
# https://oeis.org/A323253

# See also:
#   https://oeis.org/A072072
#   https://oeis.org/A071125

var range = @(1..100)

func excess (n) {
    n.bigomega - n.omega
}

func score(n) {
    var t = excess(n)
    range.first_by {|k| excess(n+k) != t }
}

say score(80566783622)           #=> 6
say score(30199064929748)        #=> 1
say score(341249411050244)       #=> 8

say [844, 74849, 671346, 8870025, 254023231417746].map(score)     #=> [4, 5, 6, 7, 8]

__END__
var n = 1

for k in (1..1e5) {
    while (isok(k) >= n) {
        say "a(#{n}) = #{k}"
        ++n
    }
}

__END__

\\ PARI code
excess(n) = bigomega(n) - omega(n);
score(n) = my(t=excess(n)); for(k=1, oo, if(excess(n+k) != t, return(k)));
upto(nn) = my(n=1); for(k=1, nn, while(score(k) >= n, print1(k, ", "); n++)); \\ ~~~~

__END__

Factors of k+j for j = 0..7, where k = 341249411050244:

[2, 2, 23, 23, 37, 10601, 411157]
[3, 3, 3, 5, 717919, 3520973]
[2, 19, 19, 19, 43, 15919, 36341]
[7, 7, 7, 994896242129]
[2, 2, 2, 3, 61, 211, 1104710237]
[13, 13, 13, 155325175717]
[2, 5, 5, 5, 31, 2591, 16994281]
[3, 11, 11, 11, 1609, 53114923]

Factors of k+j for j = 0..7, where k = 254023231417746:

[2, 3, 7, 7, 7, 174431, 707627]
[11, 11, 11, 863, 3329, 66431]
[2, 2, 13, 13, 223, 1685085251]
[3, 3, 3, 95857, 98148991]
[2, 5, 5, 5, 9001, 112886671]
[19, 19, 47, 47, 97, 3283967]
[2, 2, 2, 3, 10584301309073]
[7, 23, 23, 23, 599, 4979263]