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A290730
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Analog of A084848, replacing "quadratic residue" (X^2) with "value of X(3X-1)/2". a(n) = A290732(A290729(n)).
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3
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1, 3, 4, 6, 7, 9, 10, 12, 11, 12, 18, 21, 24, 28, 36, 40, 42, 44, 66, 77, 72, 84, 108, 120, 126, 162, 168, 216, 240, 252, 280, 264, 308, 396, 440, 462, 594, 504, 648, 720, 756, 840, 1008, 1080, 1134, 1260, 1512, 1512, 1680, 2016
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OFFSET
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1,2
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LINKS
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Hugo Pfoertner, Table of n, a(n) for n = 1..182
Andreas Enge, William Hart, Fredrik Johansson, Short addition sequences for theta functions, arXiv:1608.06810 [math.NT], 2016-2018. See Table 6.
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MATHEMATICA
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a290732[n_] := Product[{p, e} = pe; If[p <= 3, p^e, (p^e - p^(e-1))/2 + (p^(e-1) - p^(Mod[e+1, 2]))/(2*(p+1))+1], {pe, FactorInteger[n]}];
r = 2; Reap[For[j = 1, j <= 24001, j = j+1, w = a290732[j]; t = w/j; If[t < r, r = t; Sow[w]]]][[2, 1]] (* Jean-François Alcover, Oct 03 2018, after Hugo Pfoertner *)
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PROG
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(PARI) a290732(n)={my(f=factor(n)); prod(k=1, #f~, my([p, e]=f[k, ]); if(p<=3, p^e, (p^e-p^(e-1))/2+(p^(e-1)-p^((e+1)%2))/(2*(p+1))+1))}
my(r=2); for(j=1, 24001, my(w=a290732(j), t=w/j); if(t<r, r=t; print1(w, ", "))) \\ Hugo Pfoertner, Aug 26 2018
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CROSSREFS
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Cf. A000326, A085635, A084848, A290727, A290728, A290729, A290732.
Sequence in context: A184429 A248185 A130269 * A246443 A186495 A184746
Adjacent sequences: A290727 A290728 A290729 * A290731 A290732 A290733
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, Aug 10 2017
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EXTENSIONS
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More terms from Hugo Pfoertner, Aug 23 2018
a(1), a(19) and a(38) corrected by Hugo Pfoertner, Aug 26 2018
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STATUS
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approved
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