cp's OEIS Frontend

A141258 Inverse Mobius transform of the Carmichael lambda function.

%I A141258 #38 Jul 30 2022 09:46:32
%S A141258 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 A141258 27,22,29,22,31,18,23,34,23,28,37,38,27,22,41,30,43,34,29,46,47,22,49,
%U A141258 50,35,40,53,54,35,30,39,58,59,34,61,62,27,34,29,46,67,52,47,46,71,38
%N A141258 Inverse Mobius transform of the Carmichael lambda function.
%C A141258 n-th term = prime when n is prime.
%C A141258 This sequence is used in A131492 as an auxiliary sequence. - _Reinhard Zumkeller_, Feb 17 2012
%C A141258 a(n) = Sum_{k = 1..A000005(n)} A002322(A027750(n,k)). - _Reinhard Zumkeller_, Sep 02 2014
%H A141258 Enrique Pérez Herrero, <a href="/A141258/b141258.txt">Table of n, a(n) for n = 1..5000</a>
%H A141258 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 A141258 a(n) = Sum_{d|n} A002322(d).
%e A141258 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 A141258[n_] := DivisorSum[n, CarmichaelLambda[#]&];
%t A141258 Table[A141258[n],{n,1,20}] (* _Enrique Pérez Herrero_, Apr 22 2014 *)
%o A141258 (PARI) a(n) = sumdiv(n, d, lcm(znstar(d)[2])); \\ see PARI script in A002322; _Michel Marcus_, Apr 22 2014
%o A141258 (Haskell)
%o A141258 a141258 = sum . map a002322 . a027750_row
%o A141258 -- _Reinhard Zumkeller_, Sep 02 2014
%Y A141258 Cf. A002322, A027750, A051731, A061258, A131492.
%K A141258 nonn
%O A141258 1,2
%A A141258 _Gary W. Adamson_, Jun 18 2008
%E A141258 More terms from _R. J. Mathar_, Jan 19 2009