A283599 - OEIS

%I #41 Sep 08 2022 08:46:18

%S 1,2,3,5,6,7,11,13,17,18,19,20,23,29,30,31,37,41,43,47,53,59,61,67,71,

%T 73,79,80,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,

%U 163,167,173,179,180,181,191,193,197,199,211,223,225,227,229,233,239,241,251,257,263,269

%N Numbers k that divide sigma(k^2) - 1.

%C Union of prime numbers (A000040) and A283744.

%H Robert Israel, <a href="/A283599/b283599.txt">Table of n, a(n) for n = 1..10000</a>

%e 6 is in this sequence because 6 divides sigma(6^2) - 1 = 90.

%p select(n -> type((numtheory:-sigma(n^2)-1)/n, integer), [$1..1000]); # _Robert Israel_, Jun 20 2018

%t Select[Range@ 270, Divisible[DivisorSigma[1, #^2] - 1, #] &] (* _Michael De Vlieger_, Mar 15 2017 *)

%o (Magma) [n: n in [1..200] | Denominator(((SumOfDivisors(n^2))-1)/n) eq 1];

%o (PARI) for(n=1, 269, if((sigma(n^2) - 1)%n==0, print1(n,", "))) \\ _Indranil Ghosh_, Mar 14 2017

%Y Cf. A000040, A065764, A283744.

%K nonn

%O 1,2

%A _Juri-Stepan Gerasimov_, Mar 14 2017