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Imperfect numbers: Not equal to sum of proper divisors.
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%I #27 Sep 08 2022 08:45:31

%S 1,2,3,4,5,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,

%T 27,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,

%U 51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69

%N Imperfect numbers: Not equal to sum of proper divisors.

%C Imperfect numbers are either deficient numbers or abundant numbers.

%D C. A. Pickover, El prodigio de los numeros, RBA Coleccionables, 2007, p. 190.

%H Ivan Panchenko, <a href="/A132999/b132999.txt">Table of n, a(n) for n = 1..10000</a>

%H Omar E. Pol, <a href="http://www.polprimos.com">Determinacion geometrica de los numeros primos y perfectos</a>.

%F a(n) ~ n. - _Charles R Greathouse IV_, Feb 06 2015

%p with(numtheory): A132999:=n->`if`(sigma(n)=2*n,NULL,n): seq(A132999(n), n=1..100); # _Wesley Ivan Hurt_, Sep 11 2015

%o (PARI) is(n)=sigma(n,-1)!=2 \\ _Charles R Greathouse IV_, Feb 06 2015

%o (Magma) [n: n in [1..120] | not SumOfDivisors(n) eq 2*n]; // _Vincenzo Librandi_, Sep 12 2015

%Y Cf. A000396 (perfect numbers), A005100 (deficient numbers), A005101 (abundant numbers).

%K easy,nonn

%O 1,2

%A _Omar E. Pol_, Oct 13 2007