A389703 Numbers k with abundance 90: sigma(k) - 2*k = 90.

306, 2368, 28035, 46035, 49875, 107776, 654675, 33181696, 126022995, 8583970816, 11844817875, 137415098368, 5894373887955, 9803584327635, 49643912447955, 562948426694656, 8727804362534355, 18907999191244799955, 269628496255646161875, 11660838954205476372435, 151115727426814757306368, 2417851639129202791284736

Offset

1,1

Comments

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?

Also contains 11083664187510542000455635, 16849999165307800780799955, 2078341991652336345690393555, 4745838082149997379285592342527955, 1960326205542141554690232016958706407178195, 2244533631333227183087737092877226830703835955155, and 297092104984437333118450402928700081576944203259285864447955.

Also contains 2393733692416703459777364533759955 (found by Phil Carmody).

Also contains 16746855033550062880433523548655452115. - Max Alekseyev, Nov 07 2025

Links

Table of n, a(n) for n=1..22.

Max A. Alekseyev, Computing bounded solutions to linear Diophantine equations with the sum of divisors, arXiv:2601.17832 [math.NT], 2026. See p. 9, Table 1.

Carlos Rivera, Puzzle 233. A little twist, The Prime Puzzles & Problems Connection.

Mathematica

Select[Range[2^20], DivisorSigma[1, #] - 2*# == 90 &] (* Michael De Vlieger, Jan 30 2026 *)

Prog

(PARI) is(n) = sigma(n)-2*n == 90;

Crossrefs

Cf. A033880, A088831.

Sequence in context: A030030 A206679 A172966 * A223073 A064257 A221854

Adjacent sequences: A389700 A389701 A389702 * A389704 A389705 A389706

Keyword

nonn

Author

Alexander Violette, Oct 22 2025

Extensions

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

a(22) from Max Alekseyev, Mar 02 2026

Status

approved