%I #15 Jan 27 2025 02:23:55

%S 1,2,8,12,36,80,96,128,288,448,2560,6144,11264,18432,32768,53248,

%T 57344,245760,737280,1114112,2621440,4980736,22020096,23068672,

%U 25165824,66060288,75497472,96468992,436207616,939524096,1258291200,1811939328,2147483648,3774873600

%N Refactorable numbers x, such that quotient x/A000005(x) equals a power of 2.

%C This sequence is infinite since it contains all the terms of A058891. Also, 3*2^A083329(k) is a term for all k >= 1. - _Amiram Eldar_, Jan 27 2025

%H Donovan Johnson, <a href="/A078541/b078541.txt">Table of n, a(n) for n = 1..100</a>

%F a(n)/tau(a(n))=2^s with some s, tau()=A000005().

%e a(6)=80: tau(80)=10, quotient=80/10=8=2^3; certain powers of 2 do not appear as quotient, like 64, 1024, 16384.

%t Do[s=n/DivisorSigma[0, n]; If[IntegerQ[Log[2, s]], Print[{n, s, n/s}]], {n, 1, 1000000000}]

%o (PARI) isok(k) = my(r = k/numdiv(k)); denominator(r) == 1 && r >> valuation(r, 2) == 1; \\ _Amiram Eldar_, Jan 27 2025

%Y Cf. A000005, A033950, A036763, A051278, A051279, A051280, A058891, A083329.

%K nonn

%O 1,2

%A _Labos Elemer_, Dec 04 2002

%E a(29)-a(34) from _Donovan Johnson_, Jun 04 2011