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

%I A256152 #20 Jul 16 2025 20:40:14
%S A256152 22,94,115,119,214,217,265,382,497,517,527,679,745,862,889,1174,1177,
%T A256152 1207,1219,1393,1465,1501,1649,1687,1915,1942,2101,2159,2201,2359,
%U A256152 2899,2902,2995,3007,3143,3383,3401,3427,3937,4039,4054,4097,4315,4529,4537,4702,4741,5029,5065,5398,5587
%N A256152 Numbers k such that k is the product of two distinct primes and sigma(k) is a square number.
%C A256152 This sequence is the intersection of A006881 and A006532.
%H A256152 Reinhard Zumkeller, <a href="/A256152/b256152.txt">Table of n, a(n) for n = 1..1000</a>
%e A256152 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).
%t A256152 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 *)
%o A256152 (PARI) {for(i=1,10^4,if(omega(i)==2&&issquarefree(i)&&issquare(sigma(i)),print1(i,", ")))}
%o A256152 (Haskell)
%o A256152 a256152 n = a256152_list !! (n-1)
%o A256152 256152_list = filter f a006881_list where
%o A256152    f x = a010052' ((spf + 1) * (x `div` spf + 1)) == 1
%o A256152          where spf = a020639 x
%o A256152 -- _Reinhard Zumkeller_, Apr 06 2015
%Y A256152 Cf. A006881, A006532, A256149, A256150, A256151.
%Y A256152 Cf. A020639, A010052.
%K A256152 nonn
%O A256152 1,1
%A A256152 _Antonio Roldán_, Mar 16 2015