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A141258 Inverse Mobius transform of the Carmichael lambda function. 5
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 (list; graph; refs; listen; history; text; internal format)
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(A002322(A027750(n,k)): k = 1..A000005(n)).- 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.

Cf. A131492, A027750, A061258.

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

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Last modified December 15 20:00 EST 2019. Contains 330000 sequences. (Running on oeis4.)