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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The sum of aliquot divisors of prime numbers is 1.

If a^2 is an odd square for which a^2-1 = p + q with p,q primes, then p*q is a term. If m = 2^k-1 is a Mersenne prime then m*(2^k) (twice an even perfect number) is a term. If b = 2^j is a square and b-7 = 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

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Last modified October 26 14:02 EDT 2020. Contains 338027 sequences. (Running on oeis4.)