A046684 - OEIS

%I #16 Jul 23 2020 03:26:11

%S 1,2,3,4,5,7,8,9,11,13,16,17,18,19,21,23,25,27,29,31,32,33,37,39,41,

%T 43,45,47,49,51,53,55,57,59,61,64,67,69,71,72,73,77,79,81,83,87,89,91,

%U 93,95,97,98,99,100,101,103,107,109,111,113,119,121,123,125,127,128,129

%N Numbers k such that k and sum of squares of divisors of k are relatively prime.

%C All even terms are either squares or doubled squares. - _Ivan Neretin_, Dec 30 2015

%C The asymptotic density of this sequence is 0 (Dressler, 1974). - _Amiram Eldar_, Jul 23 2020

%H Ivan Neretin, <a href="/A046684/b046684.txt">Table of n, a(n) for n = 1..10000</a>

%H Robert E. Dressler, <a href="https://doi.org/10.4153/CMB-1974-019-5">On a theorem of Niven</a>, Canadian Mathematical Bulletin, Vol. 17, No. 1 (1974), pp. 109-110.

%t Select[Range[130], GCD[#, DivisorSigma[2, #]] == 1 &] (* _Ivan Neretin_, Dec 30 2015 *)

%o (PARI) isok(n) = gcd(n, sigma(n, 2)) == 1; \\ _Michel Marcus_, Jan 10 2017

%Y Cf. A001157, A046686, A046687.

%K nonn

%O 1,2

%A _Labos Elemer_