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Practical numbers whose sum of divisors is even.
2

%I #11 Dec 03 2024 11:46:01

%S 6,12,20,24,28,30,40,42,48,54,56,60,66,78,80,84,88,90,96,104,108,112,

%T 120,126,132,140,150,156,160,168,176,180,192,198,204,208,210,216,220,

%U 224,228,234,240,252,260,264,270,272,276,280,294,300,304,306,308,312,320,330,336,340,342,348,352,360,364,368,378,380

%N Practical numbers whose sum of divisors is even.

%C Practical numbers without any squares or twice squares.

%H Antti Karttunen, <a href="/A378541/b378541.txt">Table of n, a(n) for n = 1..10000</a>

%e 20 is in the sequence as it is practical (every number from 1 through sigma(20) = 42 can be written as the sum of some distinct divisors of 20) and sigma(20) = 42 is even.

%e 21 is not in the sequence as it is not practical.

%o (PARI) isA378541 = A378540;

%Y Intersection of A005153 and A028983.

%Y Setwise difference A083207 \ A353061.

%Y Cf. A378540 (characteristic function).

%K nonn,new

%O 1,1

%A _Antti Karttunen_ and _David A. Corneth_, Dec 02 2024