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A290727
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Analog of A085635, replacing "quadratic residue" (X^2) with "value of X^2+X".
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4
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1, 2, 6, 10, 14, 18, 30, 42, 66, 70, 90, 126, 198, 210, 330, 390, 450, 630, 990, 1170, 1386, 1638, 2142, 2310, 2730, 3150, 4950, 5850, 6930, 8190, 10710, 11970, 12870, 16830, 18018, 23562, 26334, 27846, 30030, 34650
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OFFSET
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1,2
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COMMENTS
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Positions where R(k) = A290731(k)/k achieves a new minimum, i.e., R(k) < R(j), j = 0..k-1, R(0) = 2.
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LINKS
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MATHEMATICA
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a290731[n_] := Product[{p, e} = pe; If[p == 2, 2^(e-1), 1+Quotient[p^(e+1), (2p+2)]], {pe, FactorInteger[n]}];
Reap[For[r = 2; k = 1, k <= 35000, k++, t = a290731[k]/k; If[t<r, r = t; Sow[k]]]][[2, 1]] (* Jean-François Alcover, Sep 03 2018, from PARI *)
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PROG
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(PARI) a290731(n)={my(f=factor(n)); prod(i=1, #f~, my([p, e]=f[i, ]); if(p==2, 2^(e-1), 1+p^(e+1)\(2*p+2)))} \\ from Andrew Howroyd
r=2; for(k=1, 40000, t=a290731(k)/k; if(t<r, r=t; print1(k, ", "))) \\ Hugo Pfoertner, Aug 23 2018
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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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