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A258250 Primitive weird numbers (pwn) (A002975) whose abundance (A033880) is a power of 2 (A000079). 6

%I

%S 70,836,4030,5830,7192,7912,10792,17272,45356,83312,91388,113072,

%T 254012,388076,786208,1713592,4145216,4559552,4632896,9928792,

%U 11547352,13086016,15126992,17999992,29465852,29581424,34869056,37111168,38546576,74899952,89283592,95327216

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

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

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

%C 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, ..., .

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

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

%H Robert G. Wilson v, <a href="/A258250/b258250.txt">Table of n, a(n) for n = 1..87</a>

%H Mark Jaybee S. Biano, Bernadette S. Estoque, Lynden Aaron D. Galera, Maria Elena S. Rulloda, Daisy Ann A. Disu, <a href="http://docplayer.net/87034980-Vol-15-no-2-april-2017-dmmmsu-cas-science-monitor.html">On Weird Numbers</a>, DMMMSU-CAS Science Monitor (2016-2017) Vol. 15 No. 2, 157-162.

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

%t (* 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[[#]] &]

%Y Cf. A002975, A000079, A033880.

%K nonn

%O 1,1

%A _Robert G. Wilson v_, Jun 19 2015

%E Corrected by _Robert G. Wilson v_, Dec 08 2015

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Last modified July 31 13:25 EDT 2021. Contains 346373 sequences. (Running on oeis4.)