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A309245
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Least number k > 0 which is not a divisor of n such that k^2 + n is a nonsquare powerful number (A102834).
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2
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682, 5, 37, 11, 1879706, 463, 11, 10, 2046, 341881, 31, 74, 70, 5519, 793, 22, 1952785824219551870, 57, 559, 338, 4580728614212333152148, 503259461, 45, 926, 190, 109, 36, 62, 436, 832836278711, 63, 88, 2451448196948930, 7037029, 36, 33
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OFFSET
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1,1
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COMMENTS
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De Koninck et al. calculated the first 50 terms of this sequence.
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LINKS
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EXAMPLE
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a(1) = 682 since 682^2 + 1 = 465125 = 5^3 * 61^2 is a nonsquare powerful number and is the smallest k > 0 such that k^2 + 1 is not a nonsquare powerful number.
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MATHEMATICA
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powerfulQ[n_] := Min@FactorInteger[n][[All, 2]] > 1; powerfulNonsquare[n_] := !IntegerQ[Sqrt[n]] && powerfulQ[n]; a[n_] := Module[{k=1}, While[Divisible[n, k] || !powerfulNonsquare[k^2 + n], k++]; k]; Table[a[n], {n, 1, 16}]
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PROG
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a(n) = for(k=1, oo, if(n%k!=0 && is_a102834(k^2+n), return(k))) \\ Felix Fröhlich, Jul 19 2019
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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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