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%I #53 Feb 08 2024 07:13:18
%S 36,100,196,225,441,484,676,1089,1156,1225,1444,1521,2116,2601,3025,
%T 3249,3364,3844,4225,4761,5476,5929,6724,7225,7396,7569,8281,8649,
%U 8836,9025,11236,12321,13225,13924,14161,14884,15129,16641,17689,17956,19881
%N Squares of the squarefree semiprimes (p^2*q^2).
%C This sequence is a member of a family of sequences directly related to A025487. First terms and known sequences are listed below: 1, A000007; 2, A000040; 4, A001248; 6, A006881; 8, A030078; 12, A054753; 16, A030514; 24, A065036; 30, A007304; 32, A050997; 36, this sequence; 48, ?; 60, ?; 64, ?; ....
%C Subsequence of A077448. The numbers in A077448 but not in here are 1, the squares of A046386, the squares of A067885, etc. - _R. J. Mathar_, Sep 12 2008
%C a(4)-a(3)=29 and a(3)+a(4)=421 are both prime. There are no other cases where the sum and difference of two members of this sequence are both prime. - _Robert Israel_ and _J. M. Bergot_, Oct 25 2019
%H T. D. Noe, <a href="/A085986/b085986.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Pri#prime_signature">Index to sequences related to prime signature</a>
%F a(n) = A006881(n)^2.
%F Sum_{n>=1} 1/a(n) = (P(2)^2 - P(4))/2 = (A085548^2 - A085964)/2 = 0.063767..., where P is the prime zeta function. - _Amiram Eldar_, Jul 06 2020
%e A006881 begins 6 10 14 15 ... so this sequence begins 36 100 196 225 ...
%t f[n_]:=Sort[Last/@FactorInteger[n]]=={2,2}; Select[Range[20000], f] (* _Vladimir Joseph Stephan Orlovsky_, Aug 14 2009 *)
%t Select[Range[200],PrimeOmega[#]==2&&SquareFreeQ[#]&]^2 (* _Harvey P. Dale_, Mar 07 2013 *)
%o (PARI) list(lim)=my(v=List(), x=sqrtint(lim\=1), t); forprime(p=2, x\2, t=p; forprime(q=2, min(x\t,p-1), listput(v, (t*q)^2))); Set(v) \\ _Charles R Greathouse IV_, Sep 22 2015
%o (PARI) is(n)=factor(n)[,2]==[2,2]~ \\ _Charles R Greathouse IV_, Oct 19 2015
%o (Magma) [k^2:k in [1..150]| IsSquarefree(k) and #PrimeDivisors(k) eq 2]; // _Marius A. Burtea_, Oct 24 2019
%Y Subsequence of A036785 and of A077448.
%Y Subsequence of A062503.
%Y Cf. A025487.
%Y Cf. A085548, A085964.
%K easy,nonn
%O 1,1
%A _Alford Arnold_, Jul 06 2003
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