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

1,1

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

Links

Table of n, a(n) for n=1..21.

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 *)

Crossrefs

Cf. A000203, A111592, A111646.

Sequence in context: A120356 A375639 A376436 * A364726 A226493 A371922

Adjacent sequences: A109742 A109743 A109744 * A109746 A109747 A109748

Keyword

nonn,more

Author

Jason Earls, Aug 10 2005

Extensions

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

a(21) from Amiram Eldar, Aug 05 2023

Status

approved