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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
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
1,1
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, ...
EXAMPLE
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.
PROG
(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, ", ")));
CROSSREFS
KEYWORD
nonn
AUTHOR
Altug Alkan, Mar 15 2016
STATUS
approved