A061258 a(n) = Sum_{d|n} d*psi(d), where psi(d) is reduced totient function, cf. A002322.

1, 3, 7, 11, 21, 21, 43, 27, 61, 63, 111, 53, 157, 129, 87, 91, 273, 183, 343, 151, 175, 333, 507, 117, 521, 471, 547, 305, 813, 261, 931, 347, 447, 819, 483, 431, 1333, 1029, 631, 327, 1641, 525, 1807, 781, 681, 1521, 2163, 373, 2101, 1563, 1095, 1103, 2757

Offset: 1

Author

Vladeta Jovovic, Apr 21 2001

Keywords

• easy
• nonn

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

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

Cf. A000005, A027750, A141258.

Programs

Haskell

a061258 n = sum $ zipWith (*) ds $ map a002322 ds
            where ds = a027750_row n
-- Reinhard Zumkeller, Sep 02 2014

Mathematica

a[n_] := DivisorSum[n, # * CarmichaelLambda[#] &]; Array[a, 100] (* Amiram Eldar, Apr 13 2024 *)

PARI

a(n) = sumdiv(n, d, d * lcm(znstar(d)[2])); \\ Amiram Eldar, Apr 13 2024

Formula

a(n) = Sum_{k = 1..A000005(n)} (A027750(n,k)*A002322(A027750(n,k))). - Reinhard Zumkeller, Sep 02 2014