A362910 Semiprimes p*q for which p <= q < p^3.

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

Offset

1,1

Comments

The terms have already been considered as "strongly semiprimes".

Links

Table of n, a(n) for n=1..57.

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

Adjacent sequences: A362907 A362908 A362909 * A362911 A362912 A362913

Keyword

nonn

Author

Alain Rocchelli, May 10 2023

Status

approved