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

1,2

Links

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

Formula

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

Mathematica

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

Prog

(Haskell)
a061258 n = sum $ zipWith (*) ds $ map a002322 ds
            where ds = a027750_row n
-- Reinhard Zumkeller, Sep 02 2014
(PARI) a(n) = sumdiv(n, d, d * lcm(znstar(d)[2])); \\ Amiram Eldar, Apr 13 2024

Crossrefs

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

Cf. A000005, A027750, A141258.

Sequence in context: A178881 A244001 A333695 * A057660 A130972 A350400

Adjacent sequences: A061255 A061256 A061257 * A061259 A061260 A061261

Keyword

easy,nonn

Author

Vladeta Jovovic, Apr 21 2001

Status

approved