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

Author

Gary W. Adamson, Jun 18 2008

Keywords

• nonn

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

Examples

			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.
		

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.

Crossrefs

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

Programs

Haskell

a141258 = sum . map a002322 . a027750_row
-- Reinhard Zumkeller, Sep 02 2014

Mathematica

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

PARI

a(n) = sumdiv(n, d, lcm(znstar(d)[2])); \\ see PARI script in A002322; Michel Marcus, Apr 22 2014

Formula

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

Extensions

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