A109321 Admirable numbers n such that the subtracted divisor is > sqrt(n).

24, 30, 84, 120, 140, 224, 234, 270, 308, 364, 476, 532, 644, 672, 1488, 1638, 2480, 3472, 3724, 4095, 5456, 5624, 6200, 6435, 6448, 8432, 9424, 11408, 14384, 15872, 18352, 20336, 21328, 23312, 24384, 26288, 29264, 29450, 30256, 33232, 35150

Offset: 1

Author

Jason Earls, Aug 20 2005

Keywords

• nonn

Comments

Solutions to sigma(x)=2(x+d) with d > sqrt(x) being a proper divisor of x. The subsequence A165772 contains most of the terms. - M. F. Hasler, Oct 11 2009

Examples

			a(2)=30 because 1+2+3+5+10+15-6 = 30 and 6 > sqrt(30) = 5.477...
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1200

Crossrefs

Cf. A111592.

Programs

Mathematica

aQ[n_] := (d = DivisorSigma[1, n] - 2n) > 0 && EvenQ[d] && Mod[n, d/2] == 0 && d < 2n && d^2 > 4n; Select[Range[35150], aQ]  (* Amiram Eldar, Sep 22 2019 *)

PARI

is_A109321(n)= my(d=sigma(n)-2*n); d>0 && bittest(d,0)==0 && d<2*n && d*d>4*n && 2*n%d==0 \\ M. F. Hasler, Oct 11 2009