A063893 - OEIS

%I #41 Sep 01 2023 21:16:30

%S 1,3,49,35713,102851,949818597,1070640001,74145779101,138452510557,

%T 158236686397,640606652893,2814821518321,9081196437853,36236716613821,

%U 97748813502577,185178952282141,433755354387133

%N Numbers k such that the sum of proper divisors or aliquot parts of k^2 is a square.

%C Numbers 640606652893, 2814821518321, 9081196437853, 36236716613821 and 97748813502577 are also terms. - _Donovan Johnson_, Mar 31 2012

%C 747834604942753, 1543596825805057, 2356096433066461, 6853335405451201 and 7704992936528497 are also terms. - _Martin Ehrenstein_, Jul 30 2023

%D A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 10.

%e 49 is a term because 49^2 = 2401 and sum of aliquot divisors of 2401: 1+7+49+343 = 400 = 20^2.

%o (PARI) s(n)=sigma(n)-n;

%o for(n=1,10^8, if(issquare(s(n^2)), print1(n, ", ")))

%Y Cf. A008847, A001065, A065764.

%K nonn,nice,hard,more

%O 1,2

%A _Jason Earls_, Aug 29 2001

%E a(6) from _Naohiro Nomoto_, Jun 06 2002

%E a(7) from _Giovanni Resta_, Jan 31 2012

%E a(8)-a(10) from _Donovan Johnson_, Mar 15 2012

%E a(11)-a(17) from _Martin Ehrenstein_, Jul 30 2023