A074985 Squares of semiprimes (A001358).
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
Offset: 1
Examples
4 is divisible by 2 (twice) and 4*4 = 16. 6 is divisible by exactly 2 and 3 and 6*6 = 36.
Links
- Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Crossrefs
Programs
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Haskell
a074985 = a000290 . a001358 -- Reinhard Zumkeller, Aug 02 2012
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Maple
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
Select[Range[200],PrimeOmega[#]==2&]^2 (* Harvey P. Dale, Oct 03 2011 *)
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PARI
is(n)=if(issquare(n,&n), isprimepower(n)==2 || factor(n)[,2]==[1,1]~, 0) \\ Charles R Greathouse IV, Oct 16 2015
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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
Formula
a(n) ~ (n log n/log log n)^2. - Charles R Greathouse IV, Oct 16 2015
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
Comments