A082663 Odd semiprimes p*q with p < q < 2*p.

15, 35, 77, 91, 143, 187, 209, 221, 247, 299, 323, 391, 437, 493, 527, 551, 589, 667, 703, 713, 851, 899, 943, 989, 1073, 1147, 1189, 1247, 1271, 1333, 1363, 1457, 1517, 1537, 1591, 1643, 1739, 1763, 1829, 1891, 1927, 1961, 2021, 2173, 2183, 2257, 2279

Offset

1,1

Comments

Numbers k such that A082647(k) = A000005(k) - 1 = 3.

A082647(p^2) = A000005(p^2) - 1 = 2, where p is odd prime.

Numbers k such that A229964(k) = 2. - Eric M. Schmidt, Oct 05 2013

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1...1000 from Vincenzo Librandi)

Example

From Charles Kusniec, Jan 01 2026: (Start)
15 = 3*5 is the smallest term because 3 and 5 are the two smallest odd primes and 3 < 5 < 2*3.
The semiprime numbers p*q can be arranged as an irregular triangle that satisfies p < q < 2*p:
q\p|   3   5   7  11  13  17  19  23
---+---------------------------------
  5|  15
  7|      35
 11|          77
 13|          91 143
 17|             187 221
 19|             209 247 323
 23|                 299 391 437
This triangle is complementary to the one in A298855 (q > 2*p).
Together, the two sequences form a disjoint partition of A046388. (End)

Mathematica

f[n_]:=Last/@FactorInteger[n]=={1, 1}&&FactorInteger[n][[1, 1]]>2&&Floor[FactorInteger[n][[2, 1]]/FactorInteger[n][[1, 1]]]==1; lst={}; Do[If[f[n], AppendTo[lst, n]], {n, 7!}]; lst (* Vladimir Joseph Stephan Orlovsky, May 19 2010 *)
pq2pQ[n_]:=Module[{fi=FactorInteger[n][[All, 1]]}, PrimeOmega[n]==2 && fi[[1]]< fi[[2]]< 2fi[[1]]]; Select[Range[1, 2301, 2], pq2pQ]//Quiet (* Harvey P. Dale, Jul 31 2021 *)

Prog

(PARI) list(lim)=my(v=List()); forprime(p=3, sqrtint(lim\=1), forprime(q=p+1, min(lim\p, 2*p), listput(v, p*q))); Set(v) \\ Charles R Greathouse IV, Mar 03 2021

Crossrefs

Cf. A000005, A056913, A046388, A082647, A229964, A298855.

Sequence in context: A098271 A234542 A242235 * A368231 A109068 A334309

Adjacent sequences: A082660 A082661 A082662 * A082664 A082665 A082666

Keyword

easy,nonn

Author

Naohiro Nomoto, May 18 2003

Extensions

New name based on a Jan 23 2004 comment from Vladeta Jovovic - Charles R Greathouse IV, Mar 03 2021

Status

approved