A348976 - OEIS

%I #10 Nov 14 2021 01:27:23

%S 1,2,3,5,5,5,7,12,11,9,11,12,13,13,14,28,17,17,19,22,20,21,23,28,29,

%T 25,39,32,29,22,31,64,32,33,34,40,37,37,38,52,41,32,43,52,50,45,47,64,

%U 55,49,50,62,53,57,54,76,56,57,59,52,61,61,72,144,64,52,67,82,68,58,71,92,73,73,78,92,76,62,79,120

%N Möbius transform of A129283, which is sum of n and its arithmetic derivative.

%H Antti Karttunen, <a href="/A348976/b348976.txt">Table of n, a(n) for n = 1..20000</a>

%F a(n) = Sum_{d|n} A008683(n/d) * A129283(d).

%F a(n) = A000010(n) + A300251(n).

%t f[p_, e_] := e/p; d[1] = 1; d[n_] := n*(1 + Plus @@ f @@@ FactorInteger[n]); a[n_] := DivisorSum[n, MoebiusMu[#]*d[n/#] &]; Array[a, 100] (* _Amiram Eldar_, Nov 13 2021 *)

%o (PARI)

%o A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));

%o A129283(n) = (n+A003415(n));

%o A348976(n) = sumdiv(n,d,moebius(n/d)*A129283(d));

%Y Cf. A000010, A003415, A008683, A129283, A300251, A347084, A348970.

%K nonn

%O 1,2

%A _Antti Karttunen_, Nov 09 2021