

A048699


Nonprime numbers whose sum of aliquot divisors (A001065) is a perfect square.


7



1, 9, 12, 15, 24, 26, 56, 75, 76, 90, 95, 119, 122, 124, 140, 143, 147, 153, 176, 194, 215, 243, 287, 332, 363, 386, 407, 477, 495, 507, 511, 524, 527, 536, 551, 575, 688, 738, 791, 794, 815, 867, 871, 892, 924, 935, 963, 992, 1075, 1083, 1159, 1196, 1199, 1295, 1304
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OFFSET

1,2


COMMENTS

The sum of aliquot divisors of prime numbers is 1.
If a^2 is an odd square for which a^21 = p + q with p,q primes, then p*q is a term. If m = 2^k1 is a Mersenne prime then m*(2^k) (twice an even perfect number) is a term. If b = 2^j is a square and b7 = 3s is a semiprime then 4s is a term.  Metin Sariyar, Apr 02 2020


LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000


EXAMPLE

a(3)=15; aliquot divisors are 1,3,5; sum of aliquot divisors = 9 and 3^2=9.


MAPLE

a := []; for n from 1 to 2000 do if sigma(n) <> n+1 and issqr(sigma(n)n) then a := [op(a), n]; fi; od: a;


MATHEMATICA

nn=1400; Select[Complement[Range[nn], Prime[Range[PrimePi[nn]]]], IntegerQ[ Sqrt[DivisorSigma[1, #]#]]&] (* Harvey P. Dale, Apr 25 2011 *)


CROSSREFS

Cf. A001065, A006532, A020477, A048698, A073040 (includes primes).
Sequence in context: A120167 A263674 A337701 * A019468 A084799 A166136
Adjacent sequences: A048696 A048697 A048698 * A048700 A048701 A048702


KEYWORD

easy,nonn


AUTHOR

Enoch Haga


STATUS

approved



