A382326
Numbers with a record ratio of nontrivial divisors to prime factors (counted with multiplicity).
Original entry on oeis.org
4, 6, 12, 24, 30, 60, 120, 180, 210, 360, 420, 840, 1260, 2310, 2520, 4620, 7560, 9240, 13860, 27720, 55440, 60060, 83160, 110880, 120120, 138600, 166320, 180180, 277200, 360360, 720720, 1081080, 1441440, 1801800, 2162160, 3063060, 3603600, 5405400, 6126120
Offset: 1
a(1) = 4: |{2}| / |{2, 2}| = 1/2.
a(2) = 6: |{2, 3}| / |{2, 3}| = 2/2.
a(3) = 12: |{2, 3, 4, 6}| / |{2, 2, 3}| = 4/3.
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my(mx=0); for(x=2, 10^5, my(f=factor(x), m=(numdiv(f)-2)/bigomega(f)); if(m>mx, mx=m; print1(x, ", ")))
A382327
Numbers with a record ratio of proper factorizations to prime factors (counted with multiplicity).
Original entry on oeis.org
4, 8, 12, 24, 36, 48, 60, 72, 120, 144, 180, 240, 288, 360, 480, 576, 720, 1080, 1440, 2160, 2520, 2880, 3600, 4320, 5040, 7200, 7560, 8640, 10080, 14400, 15120, 20160, 25200, 30240, 40320, 50400, 60480, 80640, 90720, 100800, 120960, 151200, 181440, 201600
Offset: 1
a(1) = 4: |{{2, 2}}| / |{2, 2}| = 1/2.
a(2) = 8: |{{2, 2, 2}, {2, 4}}| / |{2, 2, 2}| = 2/3.
a(3) = 12: |{{2, 2, 3}, {2, 6}, {3, 4}}| / |{2, 2, 3}| = 3/3.
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f_count(x, f=List())={my(r=x/if(#f, vecprod(Vec(f)), 1)); if(r==1, return(if(#f, 1, 0))); my(d, c=0); fordiv(r, d, if(d==1 || d==x || (#f && dmx, mx=m; print1(x, ", ")))
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