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

1,1

Comments

A number k is (2n-1)-abundant if sum_{d|k, d<k} (2*d-1) > 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.

Links

Table of n, a(n) for n=1..56.

Formula

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

Mathematica

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

Crossrefs

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

Sequence in context: A056773 A297925 A341099 * A136446 A074726 A341475

Adjacent sequences: A175834 A175835 A175836 * A175838 A175839 A175840

Keyword

nonn

Author

Vladimir Shevelev, Dec 05 2010

Extensions

More terms from Amiram Eldar, Feb 18 2019

Status

approved