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A270699
Integers n such that A084158(n) is divisible by n.
1
1, 3, 5, 11, 13, 15, 19, 29, 35, 37, 43, 53, 59, 61, 67, 75, 83, 101, 107, 109, 119, 131, 139, 149, 157, 163, 173, 179, 181, 195, 197, 211, 227, 229, 251, 255, 269, 277, 283, 293, 307, 317, 331, 347, 349, 373, 375, 379, 389, 397, 419, 421, 435, 443, 455, 461, 467, 491, 499
OFFSET
1,2
COMMENTS
For prime terms of this sequence, see A003629. Additionally, these prime numbers have the property that is in definition of A175865. Nonprime terms of this sequence are 1, 15, 35, 75, 119, 195, 255, 375, 435, 455, ...
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
EXAMPLE
3 is a term because 1^2 + 2^2 + 5^2 = 30 is divisible by 3.
5 is a term because 1^2 + 2^2 + 5^2 + 12^2 + 29^2 = 1015 is divisible by 5.
13 is a term because A084158(13) = 1351523251 is divisible by 13.
MATHEMATICA
nn = 500; s = LinearRecurrence[{5, 5, -1}, {0, 1, 5}, nn + 1]; Select[Range@ nn, Divisible[s[[# + 1]], #] &] (* Michael De Vlieger, Mar 23 2016, after Harvey P. Dale at A270699 *)
PROG
(PARI) is(n)=(Mod([0, 1, 0; 0, 0, 1; -1, 5, 5], n)^n*[0; 1; 5])[1, 1]==0 \\ Charles R Greathouse IV, Mar 21 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Altug Alkan, Mar 21 2016
STATUS
approved