A337177 Sum of the divisors d of n such that d is not equal to n/d.

0, 3, 4, 5, 6, 12, 8, 15, 10, 18, 12, 28, 14, 24, 24, 27, 18, 39, 20, 42, 32, 36, 24, 60, 26, 42, 40, 56, 30, 72, 32, 63, 48, 54, 48, 85, 38, 60, 56, 90, 42, 96, 44, 84, 78, 72, 48, 124, 50, 93, 72, 98, 54, 120, 72, 120, 80, 90, 60, 168, 62, 96, 104, 119, 84, 144, 68, 126

Offset: 1

Author

Wesley Ivan Hurt, Jan 28 2021

Keywords

• nonn
• easy

Comments

a(n) = n+1 iff n is prime or n is the square of a prime (A000430). - Bernard Schott, Jan 29 2021

Crossrefs

Cf. A000203, A037213 (with equal instead of not equal).

Programs

Mathematica

Table[Sum[k*(1 - KroneckerDelta[k, n/k]) (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 80}]

PARI

a(n) = sumdiv(n, d, d*(d!=n/d)); \\ Michel Marcus, Jan 29 2021

PARI

a(n) = sigma(n) - issquare(n)*sqrtint(n) \\ David A. Corneth, Jan 30 2021

Formula

a(n) = Sum_{d|n} d * (1 - [d = n/d]), where [ ] is the Iverson bracket.

a(n) = sigma(n) - A037213(n). - David A. Corneth, Jan 30 2021