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%I #36 Mar 02 2026 11:23:30
%S 306,2368,28035,46035,49875,107776,654675,33181696,126022995,
%T 8583970816,11844817875,137415098368,5894373887955,9803584327635,
%U 49643912447955,562948426694656,8727804362534355,18907999191244799955,269628496255646161875,11660838954205476372435,151115727426814757306368,2417851639129202791284736
%N Numbers k with abundance 90: sigma(k) - 2*k = 90.
%C If 2^k-91 is prime then 2^(k-1)*(2^k-91) is a term of this sequence. Is 306 the only even number not of this form?
%C Also contains 11083664187510542000455635, 16849999165307800780799955, 2078341991652336345690393555, 4745838082149997379285592342527955, 1960326205542141554690232016958706407178195, 2244533631333227183087737092877226830703835955155, and 297092104984437333118450402928700081576944203259285864447955.
%C Also contains 2393733692416703459777364533759955 (found by Phil Carmody).
%C Also contains 16746855033550062880433523548655452115. - _Max Alekseyev_, Nov 07 2025
%H Max A. Alekseyev, <a href="https://arxiv.org/abs/2601.17832">Computing bounded solutions to linear Diophantine equations with the sum of divisors</a>, arXiv:2601.17832 [math.NT], 2026. See p. 9, Table 1.
%H Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_233.htm">Puzzle 233. A little twist</a>, The Prime Puzzles & Problems Connection.
%t Select[Range[2^20], DivisorSigma[1, #] - 2*# == 90 &] (* _Michael De Vlieger_, Jan 30 2026 *)
%o (PARI) is(n) = sigma(n)-2*n == 90;
%Y Cf. A033880, A088831.
%K nonn
%O 1,1
%A _Alexander Violette_, Oct 22 2025
%E a(11)-a(17),a(19)-a(21) from _Alexander Violette_ and a(18) from Phil Carmody confirmed and added by _Max Alekseyev_, Nov 07 2025
%E a(22) from _Max Alekseyev_, Mar 02 2026