A187918 Largest semiprime < n^2.

6, 15, 22, 35, 46, 62, 77, 95, 119, 143, 166, 194, 221, 254, 287, 323, 358, 398, 437, 482, 527, 573, 623, 674, 723, 781, 838, 899, 959, 1018, 1082, 1154, 1219, 1294, 1366, 1441, 1517, 1594, 1679, 1763, 1843, 1934, 2021, 2105, 2206, 2302, 2395, 2498

Offset

3,1

Comments

This is to semiprimes A001358 as A053001 is to primes A000040.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 3..10000

Formula

a(n) = MAX{k in A001358 and k < n^2}.

Example

Offset is 3 because there is no semiprime less than 2^2 = 4 (as 4 is the smallest semiprime).
a(3) = 6 because 6 is the largest semiprime less than 3^2 = 9 (itself a semiprime), with only the prime 7 and the triprime 8 properly in the [6,9] interval.
a(4) = 15 < 16 = 4^2.

Mathematica

semiPrimeQ[n_] := Total[FactorInteger[n]][[2]] == 2; Table[k = n^2 - 1; While[! semiPrimeQ[k], k--]; k, {n, 3, 100}] (* T. D. Noe, Mar 15 2011 *)

Prog

(PARI) issemi(n)=bigomega(2)==2
a(n)=n*=n; while(!issemi(n--), ); n \\ Charles R Greathouse IV, Mar 16 2011

Crossrefs

Cf. A001358, A053001.

Sequence in context: A095032 A227610 A238905 * A190747 A227229 A274319

Adjacent sequences: A187915 A187916 A187917 * A187919 A187920 A187921

Keyword

nonn,easy

Author

Jonathan Vos Post, Mar 15 2011

Status

approved