A306369 - OEIS

%I #23 Dec 05 2023 08:54:19

%S 1,2,3,4,5,7,7,8,9,11,11,14,13,15,16,16,17,21,19,22,22,23,23,28,25,27,

%T 27,30,29,39,31,32,34,35,36,42,37,39,40,44,41,53,43,46,48,47,47,56,49,

%U 55,52,54,53,63,56,60,58,59,59,78,61,63,66,64,66,81,67,70,70,83,71,84,73,75,80

%N a(n) = A000010(n) + A069359(n).

%C a(n) = A291784(n) iff A001221(n) < 3, that is, iff n is in A070915.

%F a(n) = A000010(n) + A069359(n).

%F Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = A059956 + A085548 = 1.0601745... . - _Amiram Eldar_, Dec 05 2023

%e 1 is a term because A000010(1) + A069359(1) = 1 + 0.

%e 7 is a term because A000010(6) + A069359(6) = 2 + 5 = 7 = 6 + 1 = A000010(7) + A069359(7).

%t A069359[n_] := n * Plus @@ (1/FactorInteger[n][[;; , 1]]); A069359[1] = 0; a[n_] := A069359[n] + EulerPhi[n]; Array[a, 100] (* _Amiram Eldar_, Dec 05 2023 *)

%o (PARI) a(n) = eulerphi(n) + n*sumdiv(n, d, isprime(d)/d); \\ _Michel Marcus_, Feb 12 2019

%Y Cf. A000010, A001221, A069359, A070915, A291784.

%Y Cf. A059956, A085548.

%K nonn

%O 1,2

%A _Torlach Rush_, Feb 10 2019