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A060859
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Powerful numbers of the form k^2 - 1.
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5
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8, 288, 675, 9800, 235224, 332928, 1825200, 11309768, 384199200, 592192224, 4931691075, 13051463048, 221322261600, 443365544448, 865363202000, 8192480787000, 13325427460800, 15061377048200, 511643454094368
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OFFSET
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1,1
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COMMENTS
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LINKS
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FORMULA
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a(n) = k^2 - 1 and a(n) + 1 = k^2 are consecutive powerful numbers.
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EXAMPLE
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n k a(n) = k^2 - 1 a(n) + 1 = k^2
= === ========================= ==================
1 3 8 = 2^3 3^2 = 3^2
2 17 288 = 2^5 * 3^2 17^2 = 17^2
3 26 675 = 5^2 * 3^3 26^2 = 2^2 * 13^2
4 99 9800 = 2^3 * 5^2 * 7^2 99^2 = 3^4 * 11^2
5 485 235224 = 2^3 * 3^5 * 11^2 485^2 = 5^2 * 97^2
6 577 332928 = 2^7 * 3^2 * 17^2 577^2 = 577^2
(End)
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MATHEMATICA
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Select[Range[10^6]^2 - 1, Min[FactorInteger[#][[All, -1]]] > 1 &] (* Michael De Vlieger, Sep 05 2017 *)
seq[max_] := Module[{p = Union[Flatten[Table[i^2*j^3, {j, 1, max^(1/3)}, {i, 1, Sqrt[max/j^3]}]]], q, i}, q = Union[p, 2*Select[p, # <= max && OddQ[#] &]]; i = Position[Differences[q], 2] // Flatten; q[[i]]*(q[[i]] + 2)]; seq[10^10] (* Amiram Eldar, Feb 23 2024 *)
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PROG
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(PARI) isok(n) = issquare(n+1) && ispowerful(n); \\ Michel Marcus, Sep 05 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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