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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-Fran├žois 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<r, r=t; print1(w, ", "))) \\ Hugo Pfoertner, Aug 26 2018

CROSSREFS

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

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Aug 10 2017

EXTENSIONS

More terms from Hugo Pfoertner, Aug 23 2018

a(1), a(19) and a(38) corrected by Hugo Pfoertner, Aug 26 2018

STATUS

approved

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