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A236653
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Positive integers n such that n^3 divided by the digital root of n is a cube.
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2
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1, 8, 10, 19, 26, 28, 37, 44, 46, 55, 62, 64, 73, 80, 82, 91, 98, 100, 109, 116, 118, 127, 134, 136, 145, 152, 154, 163, 170, 172, 181, 188, 190, 199, 206, 208, 217, 224, 226, 235, 242, 244, 253, 260, 262, 271, 278, 280, 289, 296, 298, 307, 314, 316, 325
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OFFSET
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1,2
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LINKS
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Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).
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FORMULA
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a(n) = a(n-1)+a(n-3)-a(n-4).
G.f.: x*(8*x^3+2*x^2+7*x+1) / ((x-1)^2*(x^2+x+1)).
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EXAMPLE
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26 is in the sequence because the digital root of 26 is 8, and 26^3/8 = 2197 = 13^2.
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MATHEMATICA
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LinearRecurrence[{1, 0, 1, -1}, {1, 8, 10, 19}, 60] (* Harvey P. Dale, Sep 15 2019 *)
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PROG
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(PARI) s=[]; for(n=1, 400, d=(n-1)%9+1; if(n^3%d==0 && ispower(n^3\d, 3), s=concat(s, n))); s
(PARI) Vec(x*(8*x^3+2*x^2+7*x+1)/((x-1)^2*(x^2+x+1)) + O(x^100))
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CROSSREFS
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Cf. A010888, A236652.
Sequence in context: A153382 A157911 A090097 * A257274 A022322 A302637
Adjacent sequences: A236650 A236651 A236652 * A236654 A236655 A236656
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KEYWORD
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nonn,base,easy
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AUTHOR
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Colin Barker, Jan 29 2014
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STATUS
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approved
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