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A092356 UO-sigma multiperfect numbers: n such that A069184(n)/n is an integer. 4
1, 6, 60, 1080, 6552, 36720, 47520, 87360, 222768, 288288, 8173440, 49585536, 203558400, 683289600, 920387520, 4201148160, 25486965504, 556121548800, 1610457666048, 3633511924224, 4399770343643136, 6075071799091200, 9926754576979968, 27220195859304960, 66800080530869760, 629720915643477504 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The UO-sigma function is defined by UO-sigma(n) = A069184(n).

E.g., UO-sigma(2^4*7^2) = UnitarySigma(2^4)*sigma(7^2) = 17*57 = 969. So UO-sigma(n) = UnitarySigma(n) if n=2^r, or = sigma(n) if GCD(2,n)=1.

A UO-sigma perfect number satisfies UO-sigma(n) = k*n for some k.

The initial values of k are 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2. However, I conjecture that every positive integer >= 2 must appear.

Some interesting subsequences exist: s(n) := {a(1), a(4), a(9), a(11), ...} has the property that s(n-1)|s(n): 2*3, 2^3*3^2*7*13, 2^5*3^2*7*13*11, 2^7*3^2*7*11*13*43, 2^8*3^2*7*11*13*43*257, ...

LINKS

Table of n, a(n) for n=1..26.

Andrew Lelechenko, Numbers such that A092356(n) = 2*n

Andrew Lelechenko, Numbers such that A092356(n) = 3*n

EXAMPLE

Sequence begins: 2*3, 2^2*3*5, 2^3*3^3*5, 2^3*3^2*7*13, 2^4*3^3*5*17, 2^5*3^3*5*11, 2^6*3*5*7*13, 2^4*3^2*7*13*17, 2^5*3^2*7*13*11, 2^7*3^3*5*11*43, 2^7*3^2*7*11*13*43, ...

PROG

(PARI) is(n)=my(e=valuation(n, 2)); (sigma(n>>e) * if(e, 2^e+1, 1)) % n == 0 \\ Charles R Greathouse IV, Apr 10 2014

CROSSREFS

Cf. A091321.

Sequence in context: A126574 A061573 A248655 * A285955 A001416 A251184

Adjacent sequences:  A092353 A092354 A092355 * A092357 A092358 A092359

KEYWORD

nonn

AUTHOR

Yasutoshi Kohmoto, Mar 20 2004

EXTENSIONS

Corrected by Andrew Lelechenko, Apr 10 2014

STATUS

approved

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Last modified June 24 08:22 EDT 2017. Contains 288697 sequences.