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

Author

Jonathan Vos Post, Mar 15 2011

Keywords

• nonn
• easy

Comments

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A001358, A053001.

Programs

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 *)

PARI

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

Formula

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