A109745 Admirable numbers that set a new record for largest subtracted divisor.

12, 24, 84, 120, 270, 672, 1488, 1638, 6200, 24384, 174592, 523776, 44736512, 91963648, 100651008, 459818240, 1476304896, 10200236032, 25769607168, 51001180160, 412316073984

Offset: 1

Author

Jason Earls, Aug 10 2005

Keywords

• nonn
• more

Comments

The records set are A000203(a(n))/2 - a(n) = 2, 6, 28, 60, 90, 336, 496, 546, 1240, 8128, 21824,... - R. J. Mathar, Feb 12 2008

Crossrefs

Cf. A000203, A111592, A111646.

Programs

Mathematica

admDiv[n_] := Module[{ab = DivisorSigma[1, n] - 2*n}, If[ab > 0 && EvenQ[ab] && ab/2 < n && Divisible[n, ab/2], ab/2, 0]];
seq[nmax_] := Module[{dmax = 0, s = {}, d}, Do[d = admDiv[n]; If[d > dmax, dmax = d; AppendTo[s, n]], {n, 1, nmax}]; s]; seq[6*10^5] (* Amiram Eldar, Aug 05 2023 *)

Extensions

a(13)-a(20) from Donovan Johnson, Nov 11 2008

a(21) from Amiram Eldar, Aug 05 2023