A140668 - OEIS

%I #9 Feb 14 2019 07:46:23

%S 2,0,0,4,0,7,0,8,9,11,0,12,0,15,16,16,0,18,0,20,22,23,0,24,25,27,27,

%T 28,0,29,0,32,34,35,36,36,0,39,40,40,0,41,0,44,45,47,0,48,49,50,52,52,

%U 0,54,56,56,58,59,0,60,0,63,63,64,66,65,0,68,70,69,0,72,0,75,75,76,78,77,0,80,81,83,0,84,86,87,88,88,0

%N a(n) = n + A140664(n).

%C For n>1, a(n) = n iff mu(n) = 0; 0 if n is prime; and (n+1) iff mu(n) = 1.

%H Antti Karttunen, <a href="/A140668/b140668.txt">Table of n, a(n) for n = 1..20000</a>

%F a(n) = n + A140664(n), where A140664 = (1, -2, -3, 0, -5, 1, -7, 0, 0, 1,...)

%e a(4) = 4 = 4 + A140664(4) = 4 + 0.

%t Table[Exp[MangoldtLambda[n]]*MoebiusMu[n] + n, {n, 100}] (* _G. C. Greubel_, Feb 13 2019 *)

%o (PARI)

%o A014963(n) = ispower(n, , &n); if(isprime(n), n, 1); \\ From A014963

%o A140664(n) = (moebius(n)*A014963(n));

%o A140668(n) = (n+A140664(n)); \\ _Antti Karttunen_, Feb 13 2019

%o (Sage)

%o def A140668(n): return simplify(exp(add(moebius(d)*log(n/d) for d in divisors(n))))*moebius(n) + n

%o [A140668(n) for n in (1..100)] # _G. C. Greubel_, Feb 13 2019

%Y Cf. A140664, A008683.

%K nonn

%O 1,1

%A _Gary W. Adamson_ and _Mats Granvik_, May 20 2008

%E More terms from _Antti Karttunen_, Feb 13 2019