A389701 Numbers m with abundance 30: sigma(m) - 2*m = 30.

945, 6208, 7425, 15028, 437745, 2065408, 3428368, 20355825, 33427456, 78524145, 8587902976, 137430827008, 590295809826129707008, 827880257692739174385, 9444732963608986648576, 2417851639195173488951296

Offset

1,1

Comments

If 2^k-31 is prime, then 2^(k-1)*(2^k-31) is in this sequence.

255286886041240176056063754225, 3278298202600507814120339275775985, and 3133639738039068908629117662878760945 are some large odd terms of this sequence.

Links

Table of n, a(n) for n=1..16.

Mathematica

okQ[k_]:=DivisorSigma[1, k]-2k==30; Select[Range[4*10^6], okQ] (* James C. McMahon, Oct 28 2025 *)

Prog

(PARI) is(n) = sigma(n)-2*n == 30

Crossrefs

Deficiency k: A191363 (k=2), A125246 (k=4), A141548 (k=6), A125247 (k=8), A101223 (k=10), A141549 (k=12), A141550 (k=14), A125248 (k=16), A223608 (k=18), A223607 (k=20), A223606 (k=22), A385255 (k=24), A275702 (k=26), A389700 (k=30), A387352 (k=32), A175730 (k=42), A101259 (k=54), A275997 (k=64).

Abundance k: A088831 (k=2), A088832 (k=4), A087167 (k=6), A088833 (k=8), A223609 (k=10), A141545 (k=12), A141546 (k=14), A141547 (k=16), A223610 (k=18), A223611 (k=20), A223612 (k=22), A223613 (k=24), A275701 (k=26), A175989 (k=32), A275996 (k=64), A292626 (k=128).

Cf. A000203, A033880.

Sequence in context: A188342 A109729 A294025 * A275449 A293186 A294027

Adjacent sequences: A389698 A389699 A389700 * A389702 A389703 A389704

Keyword

nonn

Author

Alexander Violette, Oct 17 2025

Extensions

Edited, a(14) from Alexander Violette confirmed and a(12)-a(13), a(15) added by Max Alekseyev, Nov 01 2025

a(16) from Max Alekseyev, Feb 28 2026

Status

approved