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A074985
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Squares of semiprimes (A001358).
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10
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16, 36, 81, 100, 196, 225, 441, 484, 625, 676, 1089, 1156, 1225, 1444, 1521, 2116, 2401, 2601, 3025, 3249, 3364, 3844, 4225, 4761, 5476, 5929, 6724, 7225, 7396, 7569, 8281, 8649, 8836, 9025, 11236, 12321, 13225, 13924, 14161, 14641, 14884, 15129
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OFFSET
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1,1
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COMMENTS
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LINKS
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FORMULA
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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
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EXAMPLE
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4 is divisible by 2 (twice) and 4*4 = 16.
6 is divisible by exactly 2 and 3 and 6*6 = 36.
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MAPLE
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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);
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MATHEMATICA
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Select[Range[200], PrimeOmega[#]==2&]^2 (* Harvey P. Dale, Oct 03 2011 *)
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PROG
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(Haskell)
(PARI) is(n)=if(issquare(n, &n), isprimepower(n)==2 || factor(n)[, 2]==[1, 1]~, 0) \\ Charles R Greathouse IV, Oct 16 2015
(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
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CROSSREFS
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Cf. A030514 (4th powers of primes), A085986 (squares of squarefree semiprimes).
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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