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A362910 Semiprimes p*q for which p <= q < p^3. 0
4, 6, 9, 10, 14, 15, 21, 25, 33, 35, 39, 49, 51, 55, 57, 65, 69, 77, 85, 91, 95, 115, 119, 121, 133, 143, 145, 155, 161, 169, 185, 187, 203, 205, 209, 215, 217, 221, 235, 247, 253, 259, 265, 287, 289, 295, 299, 301, 305, 319, 323, 329, 335, 341, 355, 361, 365 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The terms have already been considered as "strongly semiprimes".
LINKS
Sh. T. Ishmukhametov and F. F. Sharifullina, On distribution of semiprime numbers, Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2014, No. 8, pp. 53-59. English translation, Russian Mathematics, Vol. 58, No. 8 (2014), pp. 43-48, alternative link.
FORMULA
Limit_{n->oo} n*log(a(n))/a(n) = log(3).
MAPLE
with(numtheory):
q:= n-> bigomega(n)=2 and (s-> max(s)<min(s)^3)(factorset(n)):
select(q, [$4..500])[]; # Alois P. Heinz, May 10 2023
MATHEMATICA
Select[Range[335], (f = FactorInteger[#])[[;; , 2]] == {2} || (f[[;; , 2]] == {1, 1} && f[[2, 1]] < f[[1, 1]]^3) &] (* Amiram Eldar, May 10 2023 *)
PROG
(PARI) isok(n)=if(bigomega(n)<>2, 0, my(minfact=factor(n)[1, 1], maxfact=n/minfact); maxfact<minfact^3)
select(isok, [1..500])
CROSSREFS
Cf. A001248 (subsequence), A001358, A251728.
Sequence in context: A320969 A113433 A115654 * A036326 A078972 A115652
KEYWORD
nonn
AUTHOR
Alain Rocchelli, May 10 2023
STATUS
approved

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Last modified February 26 12:26 EST 2024. Contains 370352 sequences. (Running on oeis4.)