cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A187918 Largest semiprime < n^2.

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%I A187918 #23 Mar 01 2022 07:26:28
%S A187918 6,15,22,35,46,62,77,95,119,143,166,194,221,254,287,323,358,398,437,
%T A187918 482,527,573,623,674,723,781,838,899,959,1018,1082,1154,1219,1294,
%U A187918 1366,1441,1517,1594,1679,1763,1843,1934,2021,2105,2206,2302,2395,2498
%N A187918 Largest semiprime < n^2.
%C A187918 This is to semiprimes A001358 as A053001 is to primes A000040.
%H A187918 Charles R Greathouse IV, <a href="/A187918/b187918.txt">Table of n, a(n) for n = 3..10000</a>
%F A187918 a(n) = MAX{k in A001358 and k < n^2}.
%e A187918 Offset is 3 because there is no semiprime less than 2^2 = 4 (as 4 is the smallest semiprime).
%e A187918 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.
%e A187918 a(4) = 15 < 16 = 4^2.
%t A187918 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 *)
%o A187918 (PARI) issemi(n)=bigomega(2)==2
%o A187918 a(n)=n*=n; while(!issemi(n--),); n \\ _Charles R Greathouse IV_, Mar 16 2011
%Y A187918 Cf. A001358, A053001.
%K A187918 nonn,easy
%O A187918 3,1
%A A187918 _Jonathan Vos Post_, Mar 15 2011