cp's OEIS Frontend

A050460 a(n) = Sum_{d|n, n/d=1 mod 4} d.

%I A050460 #24 Nov 06 2023 02:15:23
%S A050460 1,2,3,4,6,6,7,8,10,12,11,12,14,14,18,16,18,20,19,24,22,22,23,24,31,
%T A050460 28,30,28,30,36,31,32,34,36,42,40,38,38,42,48,42,44,43,44,60,46,47,48,
%U A050460 50,62,54,56,54,60,66,56,58,60,59,72,62,62,73,64,84,68
%N A050460 a(n) = Sum_{d|n, n/d=1 mod 4} d.
%C A050460 Not multiplicative: a(3)*a(7) <> a(21), for example.
%H A050460 Charles R Greathouse IV, <a href="/A050460/b050460.txt">Table of n, a(n) for n = 1..10000</a>
%F A050460 G.f.: Sum_{n>0} n*x^n/(1-x^(4*n)). - _Vladeta Jovovic_, Nov 14 2002
%F A050460 G.f.: Sum_{k>0} x^(4*k-3) / (1 - x^(4*k-3))^2. - _Seiichi Manyama_, Jun 29 2023
%F A050460 from _Amiram Eldar_, Nov 05 2023: (Start)
%F A050460 a(n) = A002131(n) - A050464(n).
%F A050460 a(n) = A050469(n) + A050464(n).
%F A050460 a(n) = (A002131(n) + A050469(n))/2.
%F A050460 Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = A222183. (End)
%p A050460 A050460 := proc(n)
%p A050460         a := 0 ;
%p A050460         for d in numtheory[divisors](n) do
%p A050460                 if (n/d) mod 4 = 1 then
%p A050460                         a := a+d ;
%p A050460                 end if;
%p A050460         end do:
%p A050460         a;
%p A050460 end proc:
%p A050460 seq(A050460(n),n=1..40) ; # _R. J. Mathar_, Dec 20 2011
%t A050460 a[n_] := DivisorSum[n, Boole[Mod[n/#, 4] == 1]*#&]; Array[a, 70] (* _Jean-François Alcover_, Dec 01 2015 *)
%o A050460 (PARI) a(n)=sumdiv(n,d,if(n/d%4==1,d)) \\ _Charles R Greathouse IV_, Dec 04 2013
%Y A050460 Cf. A001826, A002131, A050449, A050464, A050469, A222183.
%Y A050460 Cf. A050461, A050462, A050463.
%K A050460 nonn,easy
%O A050460 1,2
%A A050460 _N. J. A. Sloane_, Dec 23 1999