A258250 Primitive weird numbers (pwn) (A002975) whose abundance (A033880) is a power of 2 (A000079).

70, 836, 4030, 5830, 7192, 7912, 10792, 17272, 45356, 83312, 91388, 113072, 254012, 388076, 786208, 1713592, 4145216, 4559552, 4632896, 9928792, 11547352, 13086016, 15126992, 17999992, 29465852, 29581424, 34869056, 37111168, 38546576, 74899952, 89283592, 95327216

Offset: 1

Author

Robert G. Wilson v, Jun 19 2015

Keywords

• nonn

Comments

Number of terms < 10^n: 0, 1, 2, 6, 11, 15, 20, 32, 38, 48, 65, ..., .

Of the total of 499 terms < 10^11 which are pwn, only about 13% have an abundance which are powers of two.

Least term whose abundance has an exponent, e, of two > 1: 70, 836, 7192, 83312, 786208, 4145216, 98196134272, 4559552, 37111168, 22889716736, 141145802752, ?13?, 3307637248, ?15?, 154153326592, ..., .

Least term which has k prime factors, not counting multiplicity > 2: 70, 4030, 29465852, 44257207676, ..., .

Least term which has k prime factors, counting multiplicity > 2: 70, 836, 7192, 83312, 786208, 4145216, 37111168, 270788864, 2529837568, 22889716736, 141145802752, ..., .

Examples

			70 is in the sequence since sigma(70) = 144 which yields an abundance of 4 = 2^2.
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..87
• Mark Jaybee S. Biano, Bernadette S. Estoque, Lynden Aaron D. Galera, Maria Elena S. Rulloda, Daisy Ann A. Disu, On Weird Numbers, DMMMSU-CAS Science Monitor (2016-2017) Vol. 15 No. 2, 157-162.

Crossrefs

Cf. A002975, A000079, A033880.

Programs

Mathematica

(* copy the terms from A002975 and assign them to lst and then *) f[n_] := DivisorSigma[1, n] - 2n; lst[[#]] & /@ Select[ Range@ 695, IntegerQ@ Log2@ f@ lst[[#]] &]

Extensions

Corrected by Robert G. Wilson v, Dec 08 2015