Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #17 Aug 24 2023 17:02:43
%S 9,18,25,49,50,98,121,169,242,289,338,361,529,578,722,841,961,1058,
%T 1369,1681,1682,1849,1922,2209,2738,2809,3362,3481,3698,3721,4418,
%U 4489,5041,5329,5618,6241,6889,6962,7442,7921,8978,9409,10082,10201,10609,10658,11449,11881,12482,12769,13778
%N Squares of odd primes and twice squares of odd primes.
%C Essentially, the union of A001248 and A143928.
%C sigma(a(n)) = (a(n) + sqrt(a(n)) + 1) * (omega(a(n))^2 - omega(a(n)) + 1). omega(a(n)) = 2 - (a(n) mod 2). Omega(a(n)) = 3 - (a(n) mod 2). mu(a(n)) = 0. rad(a(n)) = sqrt( a(n)*omega(a(n)) ).
%e 49 is in the sequence since 49 = 7^2 (the square of an odd prime). 18 is in the sequence since 18 = 2*3^2 (twice the square of an odd prime).
%t max = 13778; Union[Prime[Range[2, PrimePi[Sqrt[max]]]]^2, 2Prime[Range[2, PrimePi[Sqrt[max/2]]]]^2] (* _Alonso del Arte_, Jul 04 2013 *)
%Y Cf. A001248, A028982, A143928.
%K nonn,easy
%O 1,1
%A _Wesley Ivan Hurt_, Jul 04 2013
%E a(38) corrected by _Georg Fischer_, Aug 24 2023