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

1,1

Links

Table of n, a(n) for n=1..27.

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 *)

Crossrefs

Cf. A000005, A071395.

Sequence in context: A053741 A303609 A052516 * A240820 A143854 A263969

Adjacent sequences: A083870 A083871 A083872 * A083874 A083875 A083876

Keyword

nonn

Author

Jason Earls, Jun 18 2003

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

Status

approved