A227279 Squares of odd primes and twice squares of odd primes.

9, 18, 25, 49, 50, 98, 121, 169, 242, 289, 338, 361, 529, 578, 722, 841, 961, 1058, 1369, 1681, 1682, 1849, 1922, 2209, 2738, 2809, 3362, 3481, 3698, 3721, 4418, 4489, 5041, 5329, 5618, 6241, 6889, 6962, 7442, 7921, 8978, 9409, 10082, 10201, 10609, 10658, 11449, 11881, 12482, 12769, 13778

Offset

1,1

Comments

Essentially, the union of A001248 and A143928.

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)) ).

Links

Table of n, a(n) for n=1..51.

Example

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).

Mathematica

max = 13778; Union[Prime[Range[2, PrimePi[Sqrt[max]]]]^2, 2Prime[Range[2, PrimePi[Sqrt[max/2]]]]^2] (* Alonso del Arte, Jul 04 2013 *)

Crossrefs

Cf. A001248, A028982, A143928.

Sequence in context: A195268 A371083 A328252 * A102042 A332551 A121282

Adjacent sequences: A227276 A227277 A227278 * A227280 A227281 A227282

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Jul 04 2013

Extensions

a(38) corrected by Georg Fischer, Aug 24 2023

Status

approved