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A292365
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Abundant numbers n such that sigma(sigma(n) - 2*n) = sigma(n).
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2
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120, 672, 1740, 7776, 19260, 20640, 21384, 21924, 22428, 25830, 31440, 55968, 93024, 101010, 106140, 143910, 151164, 198792, 246510, 309582, 326196, 411138, 421596, 428256, 499464, 523776, 590112, 639288, 697158, 870552, 941094, 958716, 1060956, 1068210, 1087776, 1100640, 1105884, 1269828
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OFFSET
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1,1
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COMMENTS
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101010 is the least squarefree term. For 6 <= k <= 8, the smallest squarefree terms with k prime factors are 101010 = 2*3*5*7*13*37, 35574630 = 2*3*5*7*13*83*157, and 401738610 = 2*3*5*7*13*31*47*101.
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LINKS
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EXAMPLE
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120 is a term because sigma(sigma(120) - 240) = sigma(360 - 240) = sigma(120).
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MATHEMATICA
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Select[Range[1.3*^6], (d = DivisorSigma[1, #]; d > 2 # && DivisorSigma[1, d - 2 #] == d) &] (* Giovanni Resta, Sep 18 2017 *)
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PROG
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(PARI) s(n) = sigma(n);
isok(n) = s(n)>2*n && s(s(n)-2*n)==s(n);
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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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