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 A270345 Composite integers n such that the sum of the Pell numbers A000129(0) + ... + A000129(n-1) is divisible by n. 1

%I

%S 4,8,16,24,32,48,64,72,96,120,128,144,168,169,192,216,240,256,264,272,

%T 288,336,360,384,385,432,480,504,512,528,544,576,600,648,672,720,768,

%U 792,816,840,864,960,961,1008,1024,1056,1080,1088,1105,1121,1152,1176,1200,1296,1320,1344

%N Composite integers n such that the sum of the Pell numbers A000129(0) + ... + A000129(n-1) is divisible by n.

%C Nonprime terms of A270342.

%C Terms that are not divisible by 4 are 169, 385, 961, 1105, 1121, 3827, 4901, 6265, 6441, 6601, 7107, 7801, 8119, ...

%e 4 is a term because 0 + 1 + 2 + 5 = 8 is divisible by 4.

%e 8 is a term because 0 + 1 + 2 + 5 + 12 + 29 + 70 + 169 = 288 is divisible by 8.

%o (PARI) a048739(n) = local(w=quadgen(8)); -1/2+(3/4+1/2*w)*(1+w)^n+(3/4-1/2*w)*(1-w)^n;

%o for(n=1, 1e3, if(a048739(n-1) % (n+1) == 0 && !isprime(n+1), print1(n+1, ", ")));

%Y Cf. A000129, A048739, A270342.

%K nonn

%O 1,1

%A _Altug Alkan_, Mar 15 2016

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Last modified January 19 10:37 EST 2021. Contains 340269 sequences. (Running on oeis4.)