A345892 a(n) = n + (n - 1) * (n - phi(n)).

1, 3, 5, 10, 9, 26, 13, 36, 33, 64, 21, 100, 25, 118, 113, 136, 33, 222, 37, 248, 201, 274, 45, 392, 145, 376, 261, 460, 57, 668, 61, 528, 449, 628, 409, 876, 73, 778, 609, 976, 81, 1272, 85, 1076, 969, 1126, 93, 1552, 385, 1520, 1001, 1480, 105, 1962, 865, 1816, 1233, 1768

Offset: 1

Author

Wesley Ivan Hurt, Jun 28 2021

Keywords

• nonn

Comments

For 1 <= k <= n, add 1 if gcd(n,k) = 1, otherwise add n. For n = 9, there are 6 numbers less than or equal to 9 that are relatively prime to 9 and 3 that are not. Then a(9) = 6*1 + 9*3 = 33.

Crossrefs

Cf. A000010 (phi), A051953 (cototient), A345891.

Programs

Mathematica

Table[n + (n - 1)*(n - EulerPhi[n]), {n, 50}]

Formula

a(n) = Sum_{k=1..n} n^(1 - floor(1/gcd(n,k))).