A270699 Integers n such that A084158(n) is divisible by n.

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

Author

Altug Alkan, Mar 21 2016

Keywords

• nonn
• easy

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, ...

Examples

			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.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000129, A003629, A084158, A175865.

Programs

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 *)

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