cp's OEIS Frontend

A074985 Squares of semiprimes (A001358).

%I A074985 #30 Nov 13 2021 22:10:28
%S A074985 16,36,81,100,196,225,441,484,625,676,1089,1156,1225,1444,1521,2116,
%T A074985 2401,2601,3025,3249,3364,3844,4225,4761,5476,5929,6724,7225,7396,
%U A074985 7569,8281,8649,8836,9025,11236,12321,13225,13924,14161,14641,14884,15129
%N A074985 Squares of semiprimes (A001358).
%C A074985 Disjoint union of 4th powers of primes, A030514, and squares of squarefree semiprimes, A085986. - _M. F. Hasler_, Nov 12 2021
%H A074985 Reinhard Zumkeller, <a href="/A074985/b074985.txt">Table of n, a(n) for n = 1..10000</a>
%F A074985 a(n) ~ (n log n/log log n)^2. - _Charles R Greathouse IV_, Oct 16 2015
%F A074985 Sum_{n>=1} 1/a(n) = (P(2)^2 + P(4))/2 = (A085548^2 + A085964)/2 = 0.1407604343..., where P is the prime zeta function. - _Amiram Eldar_, Oct 30 2020
%e A074985 4 is divisible by 2 (twice) and 4*4 = 16.
%e A074985 6 is divisible by exactly 2 and 3 and 6*6 = 36.
%p A074985 readlib(issqr): ts_kv_sp := proc(n); if (numtheory[bigomega](n)=4 and issqr(n)='true') then RETURN(n); fi; end: seq(ts_kv_sp(i), i=1..50000);
%t A074985 Select[Range[200],PrimeOmega[#]==2&]^2 (* _Harvey P. Dale_, Oct 03 2011 *)
%o A074985 (Haskell)
%o A074985 a074985 = a000290 . a001358  -- _Reinhard Zumkeller_, Aug 02 2012
%o A074985 (PARI) is(n)=if(issquare(n,&n), isprimepower(n)==2 || factor(n)[,2]==[1,1]~, 0) \\ _Charles R Greathouse IV_, Oct 16 2015
%o A074985 (PARI) list(lim)=lim=sqrtint(lim\1); my(v=List()); forprime(p=2, sqrtint(lim), forprime(q=p, lim\p, listput(v, (p*q)^2))); Set(v) \\ _Charles R Greathouse IV_, Nov 13 2021
%Y A074985 Cf. A001358, A085548, A085964.
%Y A074985 Cf. A030514 (4th powers of primes), A085986 (squares of squarefree semiprimes).
%K A074985 easy,nonn
%O A074985 1,1
%A A074985 _Jani Melik_, Oct 07 2002