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A301482 Composite numbers whose sum of aliquot parts divide the sum of the squares of their aliquot parts.

%I A301482 #28 Aug 22 2021 04:40:26
%S A301482 8,22,27,32,77,125,128,243,343,494,512,611,660,1073,1281,1331,1425,
%T A301482 2033,2048,2187,2197,2332,3125,4172,4565,4913,5293,6031,6859,8192,
%U A301482 9983,12167,13969,15818,15947,16807,17485,19683,23489,23840,24389,25241,25389,29791,32768
%N A301482 Composite numbers whose sum of aliquot parts divide the sum of the squares of their aliquot parts.
%C A301482 Semiprimes in the sequence: 22, 77, 611, 1073, 2033, 5293, 6031, 9983, 13969, 15947, 23489, 25241, 40301, 49901, 50249, 51101, 56759, 65017, 71677, 85079, 97217, 98099, 99101, .... - _Robert Israel_, Mar 29 2018
%C A301482 2^k is a term for all odd k > 1. - _Michael S. Branicky_, Aug 22 2021
%H A301482 Amiram Eldar, <a href="/A301482/b301482.txt">Table of n, a(n) for n = 1..1009</a> (terms below 10^9, terms 1..100 from Paolo P. Lava)
%e A301482 Aliquot parts of 77 are 1, 7, 11. Then (1^2 + 7^2 + 11^2)/(1 + 7 + 11) = 171/19 = 9.
%p A301482 with(numtheory): P:=proc(n)
%p A301482 if not isprime(n) and frac((add(p^2,p=divisors(n))-n^2)/(sigma(n)-n))=0
%p A301482 then n; fi; end: seq(P(i),i=2..35*10^3);
%t A301482 aQ[n_] := CompositeQ[n] && Divisible[DivisorSigma[2, n] - n^2, DivisorSigma[1, n] - n]; Select[Range[33000], aQ] (* _Amiram Eldar_, Aug 17 2019 *)
%o A301482 (PARI) isok(n) = (n!=1) && !isprime(n) && (((sigma(n,2) - n^2) % (sigma(n) - n)) == 0); \\ _Michel Marcus_, Mar 23 2018
%o A301482 (Python)
%o A301482 from sympy import divisors
%o A301482 def ok(n):
%o A301482     divs = divisors(n)[:-1]
%o A301482     return len(divs) > 1 and sum(d**2 for d in divs)%sum(divs) == 0
%o A301482 print(list(filter(ok, range(4, 32769)))) # _Michael S. Branicky_, Aug 22 2021
%Y A301482 Cf. A001065, A001157, A020487, A067558.
%Y A301482 Contains A056824.
%K A301482 nonn,easy
%O A301482 1,1
%A A301482 _Paolo P. Lava_, Mar 22 2018