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A078541 Refactorable numbers x, such that quotient x/A000005(x) equals a power of 2. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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}]

CROSSREFS

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

Sequence in context: A125712 A062290 A176961 * A285551 A135443 A143231

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

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Last modified June 22 04:06 EDT 2021. Contains 345367 sequences. (Running on oeis4.)