A078541 Refactorable numbers x, such that quotient x/A000005(x) equals a power of 2.

1, 2, 8, 12, 36, 80, 96, 128, 288, 448, 2560, 6144, 11264, 18432, 32768, 53248, 57344, 245760, 737280, 1114112, 2621440, 4980736, 22020096, 23068672, 25165824, 66060288, 75497472, 96468992, 436207616, 939524096, 1258291200, 1811939328, 2147483648, 3774873600

Offset

1,2

Comments

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

Links

Donovan Johnson, Table of n, a(n) for n = 1..100

Formula

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

Example

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.

Mathematica

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

Prog

(PARI) isok(k) = my(r = k/numdiv(k)); denominator(r) == 1 && r >> valuation(r, 2) == 1; \\ Amiram Eldar, Jan 27 2025

Crossrefs

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

Sequence in context: A125712 A062290 A176961 * A285551 A143231 A104039

Adjacent sequences: A078538 A078539 A078540 * A078542 A078543 A078544

Keyword

nonn

Author

Labos Elemer, Dec 04 2002

Extensions

a(29)-a(34) from Donovan Johnson, Jun 04 2011

Status

approved