A109788 Admirable numbers whose abundance is < 10.

12, 20, 56, 70, 88, 104, 368, 464, 650, 836, 1888, 1952, 4030, 5830, 8925, 11096, 17816, 32128, 32445, 45356, 77744, 91388, 128768, 130304, 254012, 388076, 442365, 521728, 522752, 1848964, 2087936, 2291936, 8378368, 8382464, 13174976, 29465852, 35021696, 45335936

Offset: 1

Author

Jason Earls, Aug 14 2005

Keywords

• nonn

Comments

Apparently all the abundant numbers with even abundance < 10 are admirable (checked for the first 60 terms). Of the 4 known numbers whose abundance is 10 (A223609), only the first, 40, is admirable. - Amiram Eldar, Nov 07 2019

Links

• Amiram Eldar, Table of n, a(n) for n = 1..60

Crossrefs

Cf. A033880, A111592, A111667.

Programs

Mathematica

aQ[n_] := (ab = DivisorSigma[1, n] - 2 n) > 0 && EvenQ[ab] && ab < 10 && ab/2 < n && Divisible[n, ab/2]; Select[Range[10^4], aQ] (* Amiram Eldar, Nov 07 2019 *)

PARI

for(n=1,10^9,my(ap=sigma(n)-2*n); if(ap>0 && ap<10 && ap%2==0, my(d=ap/2); if(d!=n && n%d==0, print1(n, ", ")))) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 30 2008

Extensions

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 30 2008

a(36)-a(38) from Amiram Eldar, Nov 07 2019