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

1,1

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

Links

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

Example

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

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 *)

Prog

(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

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.

Sequence in context: A209826 A107582 A213869 * A189344 A054560 A069428

Adjacent sequences: A350413 A350414 A350415 * A350417 A350418 A350419

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Dec 29 2021

Status

approved