A075730 Squares of odd semiprimes A046315, odd numbers divisible by exactly 2 primes (counted with multiplicity).
81, 225, 441, 625, 1089, 1225, 1521, 2401, 2601, 3025, 3249, 4225, 4761, 5929, 7225, 7569, 8281, 8649, 9025, 12321, 13225, 14161, 14641, 15129, 16641, 17689, 19881, 20449, 21025, 24025, 25281, 25921, 28561, 31329, 33489, 34225, 34969, 40401
Offset: 1
Examples
9 is odd and divisible by 3 (twice) and 9*9=81. 15 is odd and divisible by 3 and 5 and 15*15=225.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Crossrefs
Equals A046315(n)^2.
Programs
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Maple
readlib(issqr): ts_kv_sp_lih := proc(n); if (numtheory[bigomega](n)=4 and type(n,odd)='true' and issqr(n)='true') then RETURN(n); fi; end: seq(ts_kv_sp_lih(i), i=1..100000);
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Mathematica
Select[Range[1, 201, 2], PrimeOmega[#] == 2 &]^2 (* Amiram Eldar, Mar 22 2021 *)
Formula
Sum_{n>=1} 1/a(n) = P(2)^2/2 + P(4)/2 - P(2)/4 = 0.02769857933..., where P is the prime zeta function. - Amiram Eldar, Mar 22 2021
Extensions
Checked by Zak Seidov, Mar 08 2006