A209187 Sum of divisors of n minus cototient of n.

1, 2, 3, 5, 5, 8, 7, 11, 10, 12, 11, 20, 13, 16, 17, 23, 17, 27, 19, 30, 23, 24, 23, 44, 26, 28, 31, 40, 29, 50, 31, 47, 35, 36, 37, 67, 37, 40, 41, 66, 41, 66, 43, 60, 57, 48, 47, 92, 50, 63, 53, 70, 53, 84, 57, 88, 59, 60, 59, 124, 61, 64, 77, 95, 67, 98, 67, 90, 71, 98, 71

Offset: 1

Author

N. J. A. Sloane, Mar 05 2012

Keywords

• nonn
• easy

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000
• PrimeFan, Listing of Esoteric Integer Sequences.
• PrimeFan, Esoteric Integer Sequences [Cached copy]

Crossrefs

Cf. A000203, A051953, A065387.

Cf. A013661, A059956.

Programs

Mathematica

Table[(Plus @@ Divisors[n]) - (n - EulerPhi[n]), {n, 50}]

PARI

a(n) = sigma(n) + eulerphi(n) - n; \\ Altug Alkan, Sep 30 2017

SageMath

[sigma(n,1)+euler_phi(n)-n for n in range(1, 72)] # Stefano Spezia, Jul 20 2025

Formula

a(n) = A065387(n) - n. - Altug Alkan, Sep 30 2017

a(n) = A000203(n) - A051953(n). - Omar E. Pol, Sep 30 2017

Sum_{k=1..n} a(k) = c * n^2 / 2 + O(n*log(n)), where c = 6/Pi^2 + Pi^2/6 - 1 = 1.252861... . - Amiram Eldar, Dec 08 2023