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

Author

N. J. A. Sloane, Aug 10 2017

Keywords

• nonn

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.

Crossrefs

Cf. A085635, A084848, A290727, A290731.

Programs

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 *)

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(tHugo Pfoertner, Aug 23 2018

Formula

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

Extensions

More terms from Hugo Pfoertner, Aug 22 2018

Initial term added by Hugo Pfoertner, Aug 23 2018