A083873 Primitive abundant numbers that set a new record for number of divisors.
20, 70, 272, 550, 945, 1575, 3465, 15015, 47025, 81081, 153153, 692835, 1851759, 3633903, 6084351, 22309287, 95009481, 131339637, 277272567, 1321122231, 1516844043, 5391411025, 28816162375, 40342627325, 181667110625, 186096635725, 213239601575
Offset: 1
Keywords
Programs
-
Mathematica
abQ[n_] := DivisorSigma[-1, n] > 2; defQ[n_] := DivisorSigma[-1, n] < 2; primQ[n_] := abQ[n] && AllTrue[n/FactorInteger[n][[;; , 1]], defQ]; s = {}; dm = 0; Do[If[(d = DivisorSigma[0, n]) > dm && primQ[n], dm = d; AppendTo[s, n]], {n, 1, 10^6}]; s (* Amiram Eldar, Oct 20 2022 *)
Extensions
More terms from Lambert Herrgesell (zero815(AT)googlemail.com), Jan 02 2006
a(20)-a(24) from Donovan Johnson, Apr 09 2010
a(25)-a(27) from Donovan Johnson, Oct 21 2012