A256152 Numbers k such that k is the product of two distinct primes and sigma(k) is a square number.

22, 94, 115, 119, 214, 217, 265, 382, 497, 517, 527, 679, 745, 862, 889, 1174, 1177, 1207, 1219, 1393, 1465, 1501, 1649, 1687, 1915, 1942, 2101, 2159, 2201, 2359, 2899, 2902, 2995, 3007, 3143, 3383, 3401, 3427, 3937, 4039, 4054, 4097, 4315, 4529, 4537, 4702, 4741, 5029, 5065, 5398, 5587

Offset: 1

Author

Antonio Roldán, Mar 16 2015

Keywords

• nonn

Comments

This sequence is the intersection of A006881 and A006532.

Examples

			199 is in the sequence because 119=7*17 (the product of two distinct primes) and sigma(119)=8*18=144=12^2 (a square number).
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A006881, A006532, A256149, A256150, A256151.

Cf. A020639, A010052.

Programs

Haskell

a256152 n = a256152_list !! (n-1)
256152_list = filter f a006881_list where
   f x = a010052' ((spf + 1) * (x `div` spf + 1)) == 1
         where spf = a020639 x
-- Reinhard Zumkeller, Apr 06 2015

Mathematica

f[n_] := Block[{pf = FactorInteger@ n}, Max @@ Last /@ pf == 1 && Length@ pf == 2]; Select[Range@ 6000, IntegerQ@ Sqrt@ DivisorSigma[1, #] && f@ # &] (* Michael De Vlieger, Mar 17 2015 *)

PARI

{for(i=1,10^4,if(omega(i)==2&&issquarefree(i)&&issquare(sigma(i)),print1(i,", ")))}