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A318170
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Composite numbers k such that A008480(k) = k.
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1
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OFFSET
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1,1
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COMMENTS
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Knopfmacher and Luca proved that this sequence is finite.
These numbers are named "prime-factor-perfect numbers" by Knopfmacher and Mays and "prime-perfect numbers" by Knopfmacher and Luca.
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LINKS
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Arnold Knopfmacher and Florian Luca, On prime-perfect numbers, International Journal of Number Theory, Vol. 7, No. 7 (2011), pp. 1705-1716
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EXAMPLE
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1781030694643200 = 2^9 * 3^5 * 5^2 * 7^2 * 11^2 * 13 * 17 * 19 * 23 is in the sequence since multinomial(9+5+2+2+2+1+1+1+1,9,5,2,2,2,1,1,1,1) = 1781030694643200.
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MATHEMATICA
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mul[w_] := Total[w]!/Times @@ (w!); f[n_] := Select[ IntegerPartitions@ n, # == Reverse@ Sort[ Last /@ FactorInteger[mul[#]]] &]; Sort[mul /@ Flatten[f /@ Range[2, 30], 1]] (* terms with sum of exponents in prime factorization <= 30, Giovanni Resta, Aug 20 2018 *)
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CROSSREFS
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KEYWORD
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nonn,more,fini
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AUTHOR
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STATUS
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approved
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