A270699 - OEIS

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

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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

Cf. A000129, A003629, A084158, A175865.

Sequence in context: A329629 A340019 A302521 * A260398 A065396 A020620

Adjacent sequences: A270696 A270697 A270698 * A270700 A270701 A270702

KEYWORD

nonn,easy

AUTHOR

Altug Alkan, Mar 21 2016

STATUS

approved