A246454 Numbers k that divide 2*sigma(k).

1, 2, 6, 24, 28, 120, 496, 672, 4320, 4680, 8128, 26208, 30240, 32760, 523776, 2178540, 8910720, 17428320, 20427264, 23569920, 33550336, 45532800, 91963648, 142990848, 197064960, 459818240, 1379454720, 1476304896, 8583644160, 8589869056, 10200236032

Offset: 1

Author

Jaroslav Krizek, Aug 26 2014

Keywords

• nonn

Comments

Numbers k such that 2*A000203(k) / k is an integer.

Union of A007691 (multiply-perfect numbers) and A159907 (numbers with half-integral abundancy index).

Examples

			Number 24 is in the sequence because 24 divides 2*sigma(24); 24 divides 2*60.
		

Links

• Jens Kruse Andersen, Table of n, a(n) for n = 1..55

Crossrefs

Cf. A000203, A007691, A159907.

Programs

Magma

[n: n in [1..1000000] | Denominator(2*(SumOfDivisors(n))/n) eq 1];

PARI

for(n=1,10^8,if((2*sigma(n))%n==0,print1(n,", "))) \\ Derek Orr, Aug 26 2014