A306369 a(n) = A000010(n) + A069359(n).

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

Offset: 1

Author

Torlach Rush, Feb 10 2019

Keywords

• nonn

Comments

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

Examples

			1 is a term because A000010(1) + A069359(1) = 1 + 0.
7 is a term because A000010(6) + A069359(6) = 2 + 5 = 7 = 6 + 1 = A000010(7) + A069359(7).
		

Crossrefs

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

Cf. A059956, A085548.

Programs

Mathematica

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 *)

PARI

a(n) = eulerphi(n) + n*sumdiv(n, d, isprime(d)/d); \\ Michel Marcus, Feb 12 2019

Formula

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

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