A290730 Analog of A084848, replacing "quadratic residue" (X^2) with "value of X(3X-1)/2". a(n) = A290732(A290729(n)).

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

Offset: 1

Author

N. J. A. Sloane, Aug 10 2017

Keywords

• nonn

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.

Crossrefs

Cf. A000326, A085635, A084848, A290727, A290728, A290729, A290732.

Programs

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 *)

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(tHugo Pfoertner, Aug 26 2018

Extensions

More terms from Hugo Pfoertner, Aug 23 2018

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