

A290730


Analog of A084848, replacing "quadratic residue" (X^2) by "value of X(3X1)/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
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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], 20162018. See Table 6.


MATHEMATICA

a290732[n_] := Product[{p, e} = pe; If[p <= 3, p^e, (p^e  p^(e1))/2 + (p^(e1)  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]] (* JeanFrançois 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^ep^(e1))/2+(p^(e1)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



