|
| |
|
|
A048699
|
|
Nonprime numbers whose sum of aliquot divisors (A001065) is a perfect square.
|
|
8
|
|
|
|
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
|
|
|
|
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
|
|
|
|
KEYWORD
|
easy,nonn
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
