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Analog of A084848, replacing "quadratic residue" (X^2) with "value of X^2+X".
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%I #24 Sep 13 2018 13:19:08

%S 1,1,2,3,4,4,6,8,12,12,12,16,24,24,36,42,44,48,72,84,96,112,144,144,

%T 168,176,264,308,288,336,432,480,504,648,672,864,960,1008,1008,1056,

%U 1232,1584,1760,1848,2376,2016,2592

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

%H Hugo Pfoertner, <a href="/A290728/b290728.txt">Table of n, a(n) for n = 1..116</a>

%H Andreas Enge, William Hart, Fredrik Johansson, <a href="http://arxiv.org/abs/1608.06810">Short addition sequences for theta functions</a>, arXiv:1608.06810 [math.NT], 2016-2018. See Table 5.

%F a(n) = A290731(A290727(n)) - _Hugo Pfoertner_, Aug 23 2018

%t a290731[n_] := Product[{p, e} = pe; If[p==2, 2^(e-1), 1 + Quotient[p^(e+1), (2p + 2)]], {pe, FactorInteger[n]}];

%t 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 *)

%o (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_

%o r=2;for(k=1,200000,v=a290731(k);t=v/k;if(t<r,r=t;print1(v,", "))) \\ _Hugo Pfoertner_, Aug 23 2018

%Y Cf. A085635, A084848, A290727, A290731.

%K nonn

%O 1,3

%A _N. J. A. Sloane_, Aug 10 2017

%E More terms from _Hugo Pfoertner_, Aug 22 2018

%E Initial term added by _Hugo Pfoertner_, Aug 23 2018