A256152 Numbers n such that n is the product of two distinct primes and sigma(n) 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

1,1

Comments

This sequence is the intersection of A006881 and A006532.

Links

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

Example

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).

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 *)

Prog

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

Crossrefs

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

Cf. A020639, A010052.

Sequence in context: A041944 A230357 A145769 * A159539 A178999 A272378

Adjacent sequences: A256149 A256150 A256151 * A256153 A256154 A256155

Keyword

nonn

Author

Antonio Roldán, Mar 16 2015

Status

approved