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 A290730 Analog of A084848, replacing "quadratic residue" (X^2) by "value of X(3X-1)/2". a(n) = A290732(A290729(n)). 3
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS 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. MATHEMATICA 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 *) PROG (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

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Last modified December 9 19:51 EST 2019. Contains 329879 sequences. (Running on oeis4.)