A290728 Analog of A084848, replacing "quadratic residue" (X^2) with "value of X^2+X".

1, 1, 2, 3, 4, 4, 6, 8, 12, 12, 12, 16, 24, 24, 36, 42, 44, 48, 72, 84, 96, 112, 144, 144, 168, 176, 264, 308, 288, 336, 432, 480, 504, 648, 672, 864, 960, 1008, 1008, 1056, 1232, 1584, 1760, 1848, 2376, 2016, 2592

Offset

1,3

Links

Hugo Pfoertner, Table of n, a(n) for n = 1..116

Andreas Enge, William Hart, Fredrik Johansson, Short addition sequences for theta functions, arXiv:1608.06810 [math.NT], 2016-2018. See Table 5.

Formula

a(n) = A290731(A290727(n)) - Hugo Pfoertner, Aug 23 2018

Mathematica

a290731[n_] := Product[{p, e} = pe; If[p==2, 2^(e-1), 1 + Quotient[p^(e+1), (2p + 2)]], {pe, FactorInteger[n]}];
Reap[For[r = 2; k = 1, k <= 200000, k++, v = a290731[k]; t = v/k; If[t < r, r = t; Sow[v]]]][[2, 1]] (* Jean-François Alcover, Sep 13 2018, from PARI *)

Prog

(PARI) a290731(n)={my(f=factor(n)); prod(i=1, #f~, my([p, e]=f[i, ]); if(p==2, 2^(e-1), 1+p^(e+1)\(2*p+2)))} \\ from Andrew Howroyd
r=2; for(k=1, 200000, v=a290731(k); t=v/k; if(t<r, r=t; print1(v, ", "))) \\ Hugo Pfoertner, Aug 23 2018

Crossrefs

Cf. A085635, A084848, A290727, A290731.

Sequence in context: A331527 A326575 A331848 * A296116 A017832 A347713

Adjacent sequences: A290725 A290726 A290727 * A290729 A290730 A290731

Keyword

nonn

Author

N. J. A. Sloane, Aug 10 2017

Extensions

More terms from Hugo Pfoertner, Aug 22 2018

Initial term added by Hugo Pfoertner, Aug 23 2018

Status

approved