A350416 - OEIS

%I #24 Jun 11 2022 14:05:30

%S 6300,8820,9900,11700,12600,14700,15300,17100,17640,18900,19404,19800,

%T 20700,21780,22050,22932,23400,25200,26100,26460,27900,29400,29700,

%U 29988,30420,30492,30600,31500,33300,33516,34200,35100,35280,36300,36900,37800,38700,38808

%N Numbers with exactly 9 semiprime divisors.

%C Numbers with exactly four distinct prime divisors (cf. A033993), one of which has multiplicity 1 and the others at least 2. - _David A. Corneth_, Jun 10 2022

%H David A. Corneth, <a href="/A350416/b350416.txt">Table of n, a(n) for n = 1..10000</a>

%e 6300 is in the sequence as 4, 6, 9, 10, 14, 15, 21, 25, 35 are the exactly 9 of its semiprime divisors. - _David A. Corneth_, Jun 10 2022

%t q[n_] := DivisorSum[n, 1 &, PrimeOmega[#] == 2 &] == 9; Select[Range[40000], q] (* _Amiram Eldar_, Dec 30 2021 *)

%t spd9Q[n_]:=Count[Divisors[n],_?(PrimeOmega[#]==2&)]==9; Select[Range[ 40000],spd9Q] (* _Harvey P. Dale_, Jun 09 2022 *)

%o (PARI) isok(k) = sumdiv(k, d, bigomega(d)==2) == 9; \\ _Michel Marcus_, Dec 30 2021

%o (PARI) is(n)= if(n==1, return(0)); my(f = vecsort(factor(n)[,2])); #f == 4 && f[1] == 1 && f[2]>=2 \\ _David A. Corneth_, Jun 10 2022

%Y Numbers with exactly k semiprime divisors: A346041 (k=1), A345381 (k=2), A345382 (k=3), A350371 (k=4), A350372 (k=5), A350373 (k=6), A350374 (k=7), A350375 (k=8), this sequence (k=9).

%Y Cf. A033993, A220264.

%K nonn,easy

%O 1,1

%A _Wesley Ivan Hurt_, Dec 29 2021