

A256152


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


5



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
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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 !! (n1)
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



