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A323329
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Lesser of amicable pair m < n defined by t(n) = m and t(m) = n where t(n) = psi(n) - n and psi(n) = A001615(n) is the Dedekind psi function.
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4
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1330, 2660, 3850, 5320, 6650, 7700, 10640, 11270, 13300, 14950, 15400, 18550, 19250, 21280, 22540, 26600, 29900, 30800, 33250, 37100, 38500, 42560, 45080, 53200, 59800, 61600, 66500, 73370, 74200, 74750, 77000, 78890, 85120, 90160, 92750, 96250, 106400, 119600
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OFFSET
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1,1
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COMMENTS
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t(n) = psi(n) - n is the sum of aliquot divisors of n, d, such that n/d is squarefree. Penney & Pomerance proposed a problem to show that the "pseudo-aliquot" sequence related to this function is unbounded. This sequence lists number with pseudo-aliquot sequence of cycle 2. The sequence that is analogous to perfect numbers is A033845.
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LINKS
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David E. Penney and Carl Pomerance, Problem 10323, The American Mathematical Monthly, Volume 100, No. 7 (1993), p. 688.
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MATHEMATICA
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psi[n_] := n*Times@@(1+1/Transpose[FactorInteger[n]][[1]]); t[n_]:= psi[n] - n; s={}; Do[n=t[m]; If[n>m && t[n]==m, AppendTo[s, m]], {m, 1, 120000}]; s
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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