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

4, 8, 16, 24, 32, 48, 64, 72, 96, 120, 128, 144, 168, 169, 192, 216, 240, 256, 264, 272, 288, 336, 360, 384, 385, 432, 480, 504, 512, 528, 544, 576, 600, 648, 672, 720, 768, 792, 816, 840, 864, 960, 961, 1008, 1024, 1056, 1080, 1088, 1105, 1121, 1152, 1176, 1200, 1296, 1320, 1344

Offset: 1

Author

Altug Alkan, Mar 15 2016

Keywords

• nonn

Comments

Nonprime terms of A270342.

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

Examples

			4 is a term because 0 + 1 + 2 + 5 = 8 is divisible by 4.
8 is a term because 0 + 1 + 2 + 5 + 12 + 29 + 70 + 169 = 288 is divisible by 8.
		

Crossrefs

Cf. A000129, A048739, A270342.

Programs

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