A061258 - OEIS

%I #13 Apr 13 2024 05:16:26

%S 1,3,7,11,21,21,43,27,61,63,111,53,157,129,87,91,273,183,343,151,175,

%T 333,507,117,521,471,547,305,813,261,931,347,447,819,483,431,1333,

%U 1029,631,327,1641,525,1807,781,681,1521,2163,373,2101,1563,1095,1103,2757

%N a(n) = Sum_{d|n} d*psi(d), where psi(d) is reduced totient function, cf. A002322.

%H Reinhard Zumkeller, <a href="/A061258/b061258.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = Sum_{k = 1..A000005(n)} (A027750(n,k)*A002322(A027750(n,k))). - _Reinhard Zumkeller_, Sep 02 2014

%t a[n_] := DivisorSum[n, # * CarmichaelLambda[#] &]; Array[a, 100] (* _Amiram Eldar_, Apr 13 2024 *)

%o (Haskell)

%o a061258 n = sum $ zipWith (*) ds $ map a002322 ds

%o             where ds = a027750_row n

%o -- _Reinhard Zumkeller_, Sep 02 2014

%o (PARI) a(n) = sumdiv(n, d, d * lcm(znstar(d)[2])); \\ _Amiram Eldar_, Apr 13 2024

%Y Cf. A002322, A057660, A001001, A060640, A061259.

%Y Cf. A000005, A027750, A141258.

%K easy,nonn

%O 1,2

%A _Vladeta Jovovic_, Apr 21 2001