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A092356 UO-sigma multiperfect numbers: n such that A069184(n)/n is an integer.

%I A092356 #24 Apr 19 2016 01:07:34
%S A092356 1,6,60,1080,6552,36720,47520,87360,222768,288288,8173440,49585536,
%T A092356 203558400,683289600,920387520,4201148160,25486965504,556121548800,
%U A092356 1610457666048,3633511924224,4399770343643136,6075071799091200,9926754576979968,27220195859304960,66800080530869760,629720915643477504
%N A092356 UO-sigma multiperfect numbers: n such that A069184(n)/n is an integer.
%C A092356 The UO-sigma function is defined by UO-sigma(n) = A069184(n).
%C A092356 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.
%C A092356 A UO-sigma perfect number satisfies UO-sigma(n) = k*n for some k.
%C A092356 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.
%C A092356 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, ...
%H A092356 Andrew Lelechenko, <a href="/A092356/a092356_2.txt">Numbers such that A092356(n) = 2*n</a>
%H A092356 Andrew Lelechenko, <a href="/A092356/a092356_1.txt">Numbers such that A092356(n) = 3*n</a>
%e A092356 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, ...
%o A092356 (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
%Y A092356 Cf. A091321.
%K A092356 nonn
%O A092356 1,2
%A A092356 _Yasutoshi Kohmoto_, Mar 20 2004
%E A092356 Corrected by _Andrew Lelechenko_, Apr 10 2014