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A045795
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Unitary-sigma sigma multiply perfect numbers: numbers k such that A061765(k) = m*k for some integer m.
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3
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1, 2, 4, 8, 10, 16, 24, 27, 30, 54, 63, 64, 108, 126, 165, 238, 252, 360, 432, 504, 512, 660, 864, 952, 1008, 1536, 1728, 2016, 2464, 2640, 4032, 4096, 5544, 10560, 13824, 16728, 17640, 23040, 32256, 45500, 47360, 60928, 65536, 110592, 152064, 153600
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OFFSET
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1,2
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LINKS
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EXAMPLE
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Sigma(10) = 18 = 2*3^2, usigma(18) = (2+1)*(9+1) = 30, divisible by 10, so 10 is in the sequence.
Sigma(24) = 60 = 2^2*3*5, usigma(60) = 5*4*6 = 120, divisible by 24, so 24 is in the sequence.
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MATHEMATICA
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q[n_] := Divisible[Times @@ (1 + Power @@@ FactorInteger[DivisorSigma[1, n]]), n]; Select[Range[200000], q] (* Amiram Eldar, Aug 26 2022 *)
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PROG
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(PARI) for(n=1, 10^9, s=sigma(n); om=omega(s); f=factorint(s); pr=1; for(j=1, om, pr=pr*(f[j, 1]^f[j, 2]+1)); if(pr%n==0, print(n))) \\ Donovan Johnson, Mar 12 2013
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Missing first term added and offset corrected by Donovan Johnson, Mar 12 2013
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STATUS
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approved
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