A350416 Numbers with exactly 9 semiprime divisors.

6300, 8820, 9900, 11700, 12600, 14700, 15300, 17100, 17640, 18900, 19404, 19800, 20700, 21780, 22050, 22932, 23400, 25200, 26100, 26460, 27900, 29400, 29700, 29988, 30420, 30492, 30600, 31500, 33300, 33516, 34200, 35100, 35280, 36300, 36900, 37800, 38700, 38808

Offset: 1

Author

Wesley Ivan Hurt, Dec 29 2021

Keywords

• nonn
• easy

Comments

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

Examples

			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
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000

Crossrefs

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).

Cf. A033993, A220264.

Programs

Mathematica

q[n_] := DivisorSum[n, 1 &, PrimeOmega[#] == 2 &] == 9; Select[Range[40000], q] (* Amiram Eldar, Dec 30 2021 *)
spd9Q[n_]:=Count[Divisors[n],?(PrimeOmega[#]==2&)]==9; Select[Range[ 40000],spd9Q] (* _Harvey P. Dale, Jun 09 2022 *)

PARI

isok(k) = sumdiv(k, d, bigomega(d)==2) == 9; \\ Michel Marcus, Dec 30 2021

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