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A175837 (2n-1)-abundant numbers 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 12 18:58 EDT 2021. Contains 342932 sequences. (Running on oeis4.)