A175837 (2n-1)-abundant numbers.

12, 18, 24, 30, 36, 40, 42, 48, 54, 56, 60, 66, 70, 72, 78, 80, 84, 88, 90, 96, 100, 102, 108, 112, 114, 120, 126, 132, 138, 140, 144, 150, 156, 160, 162, 168, 174, 176, 180, 186, 192, 196, 198, 200, 204, 208, 210, 216, 220, 222, 224, 228, 234, 240, 246, 252

Offset: 1

Author

Vladimir Shevelev, Dec 05 2010

Keywords

• nonn

Comments

A number k is (2n-1)-abundant if sum_{d|k, d 2*k-1, a specialization of the definition in A175522.

Adding 2k-1 on both sides of the condition yields the equivalent condition A129246(k) > 2*(2k-1).

Adding 2k-1 on both sides also yields sum_{d|k} (2*d-1) > 2*(2k-1), equivalent to 2*sum_{d|k}d - tau(k) > 2*(2k-1) or sigma(k) > 2k-1+tau(k)/2, equivalent to A033880(k) > tau(k)/2-1.

Crossrefs

Cf. A175522, A033880, A000203, A005100, A005101.

Programs

Mathematica

aQ[n_] := DivisorSum[n, 2#-1&, # 2n-1; Select[Range[252], aQ] (* Amiram Eldar, Feb 18 2019 *)

Formula

A175837 = { n | A033880(n) > A000005(n)/2-1 }.

Extensions

More terms from Amiram Eldar, Feb 18 2019