Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #38 Jul 30 2022 09:46:32
%S 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,
%T 27,22,29,22,31,18,23,34,23,28,37,38,27,22,41,30,43,34,29,46,47,22,49,
%U 50,35,40,53,54,35,30,39,58,59,34,61,62,27,34,29,46,67,52,47,46,71,38
%N Inverse Mobius transform of the Carmichael lambda function.
%C n-th term = prime when n is prime.
%C This sequence is used in A131492 as an auxiliary sequence. - _Reinhard Zumkeller_, Feb 17 2012
%C a(n) = Sum_{k = 1..A000005(n)} A002322(A027750(n,k)). - _Reinhard Zumkeller_, Sep 02 2014
%H Enrique Pérez Herrero, <a href="/A141258/b141258.txt">Table of n, a(n) for n = 1..5000</a>
%H W. D. Banks and F. Luca, <a href="https://www.emis.de/journals/AM/06-1/am1278.pdf">On integers with a special divisibility property</a>, Archivum Mathematicum (BRNO) 42 (2006) pp 31-42.
%F a(n) = Sum_{d|n} A002322(d).
%e 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.
%t A141258[n_] := DivisorSum[n, CarmichaelLambda[#]&];
%t Table[A141258[n],{n,1,20}] (* _Enrique Pérez Herrero_, Apr 22 2014 *)
%o (PARI) a(n) = sumdiv(n, d, lcm(znstar(d)[2])); \\ see PARI script in A002322; _Michel Marcus_, Apr 22 2014
%o (Haskell)
%o a141258 = sum . map a002322 . a027750_row
%o -- _Reinhard Zumkeller_, Sep 02 2014
%Y Cf. A002322, A027750, A051731, A061258, A131492.
%K nonn
%O 1,2
%A _Gary W. Adamson_, Jun 18 2008
%E More terms from _R. J. Mathar_, Jan 19 2009