A141258 Inverse Mobius transform of the Carmichael lambda function.

1, 2, 3, 4, 5, 6, 7, 6, 9, 10, 11, 10, 13, 14, 11, 10, 17, 18, 19, 16, 15, 22, 23, 14, 25, 26, 27, 22, 29, 22, 31, 18, 23, 34, 23, 28, 37, 38, 27, 22, 41, 30, 43, 34, 29, 46, 47, 22, 49, 50, 35, 40, 53, 54, 35, 30, 39, 58, 59, 34, 61, 62, 27, 34, 29, 46, 67, 52, 47, 46, 71, 38

Offset

1,2

Comments

n-th term = prime when n is prime.

This sequence is used in A131492 as an auxiliary sequence. - Reinhard Zumkeller, Feb 17 2012

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

Links

Enrique Pérez Herrero, Table of n, a(n) for n = 1..5000

W. D. Banks and F. Luca, On integers with a special divisibility property, Archivum Mathematicum (BRNO) 42 (2006) pp 31-42.

Formula

a(n) = Sum_{d|n} A002322(d).

Example

a(6) = 6 = (1, 1, 1, 0, 0, 1) dot (1, 1, 2, 2, 4, 2) = (1 + 1 + 2 + 0 + 0 + 2); where (1, 1, 1, 0, 0, 1) = row 6 of triangle A051731.

Mathematica

A141258[n_] := DivisorSum[n, CarmichaelLambda[#]&];
Table[A141258[n], {n, 1, 20}] (* Enrique Pérez Herrero, Apr 22 2014 *)

Prog

(PARI) a(n) = sumdiv(n, d, lcm(znstar(d)[2])); \\ see PARI script in A002322; Michel Marcus, Apr 22 2014
(Haskell)
a141258 = sum . map a002322 . a027750_row
-- Reinhard Zumkeller, Sep 02 2014

Crossrefs

Cf. A002322, A027750, A051731, A061258, A131492.

Sequence in context: A161658 A066853 A264856 * A117656 A101918 A291169

Adjacent sequences: A141255 A141256 A141257 * A141259 A141260 A141261

Keyword

nonn

Author

Gary W. Adamson, Jun 18 2008

Extensions

More terms from R. J. Mathar, Jan 19 2009

Status

approved