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A045795
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Unitary-sigma sigma multiply perfect numbers n such that usigma(sigma(n)) = m*n for some integer m, where if sigma(n) = product p(i)^r(i) then usigma(sigma(n)) = product (p(i)^r(i)+1).
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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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Donovan Johnson, Table of n, a(n) for n = 1..100
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EXAMPLE
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For example, 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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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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Cf. A045796, A034448.
Sequence in context: A025612 A102248 A161374 * A083655 A097210 A097214
Adjacent sequences: A045792 A045793 A045794 * A045796 A045797 A045798
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KEYWORD
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nonn
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AUTHOR
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Yasutoshi Kohmoto (zbi74583(AT)boat.zero.ad.jp)
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EXTENSIONS
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Corrected and extended by Jud McCranie, Oct 28 2001
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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