cp's OEIS Frontend

A355543 Numbers k such that the sum of the squares of the odd divisors of k (A050999) is divisible by k.

%I A355543 #8 Jul 07 2022 08:12:55
%S A355543 1,65,130,175,260,350,525,1050,1105,2100,2210,4420,5425,8840,10850,
%T A355543 16275,20737,21700,30225,32045,32550,41474,60450,64090,65100,70525,
%U A355543 82948,86025,103685,120900,128180,130200,141050,171275,172050,200725,207370,207553,211575
%N A355543 Numbers k such that the sum of the squares of the odd divisors of k (A050999) is divisible by k.
%C A355543 If k is an odd term > 1 then 2*k is also in the sequence.
%H A355543 Amiram Eldar, <a href="/A355543/b355543.txt">Table of n, a(n) for n = 1..1000</a>
%e A355543 65 is a term since A050999(65) = 4420 = 65 * 68 is divisible by 65.
%t A355543 f[p_, e_] := If[p == 2, 1, (p^(2*e + 2) - 1)/(p^2 - 1)]; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; Select[Range[10^5], Divisible[s[#], #] &]
%o A355543 (PARI) f(n) = sumdiv(n, d, if(d%2==1, d^2, 0 ) ); \\ A050999
%o A355543 isok(k) = !(f(k) % k); \\ _Michel Marcus_, Jul 07 2022
%Y A355543 Cf. A050999.
%Y A355543 Similar sequences: A007691, A046762.
%K A355543 nonn
%O A355543 1,2
%A A355543 _Amiram Eldar_, Jul 06 2022