A232324 n(n+1)/2 modulo sigma(n).

0, 0, 2, 3, 3, 9, 4, 6, 6, 1, 6, 22, 7, 9, 0, 12, 9, 15, 10, 0, 7, 1, 12, 0, 15, 15, 18, 14, 15, 33, 16, 24, 33, 1, 6, 29, 19, 21, 52, 10, 21, 39, 22, 66, 21, 1, 24, 60, 28, 66, 30, 6, 27, 45, 28, 36, 53, 1, 30, 150, 31, 33, 40, 48, 45, 51, 34, 78, 15, 37, 36

Offset: 1

Author

Jaroslav Krizek, Nov 25 2013

Keywords

• nonn

Comments

Also antisigma(n) modulo sigma(n). Antisigma(n) = A024816(n) = the sum of the nondivisors of n that are between 1 and n, sigma(n) = A000203(n) = the sum of the divisors of n.

a(n) = 0 for numbers from A076617, a(n) = 1 for numbers from A232540, a(n) = n for numbers from A232538.

Examples

			For n=10, a(10) = antisigma(10) mod sigma(10) = 37 mod 18 = 1.
		

Links

• Jaroslav Krizek, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000203, A076617, A024816, A232538, A232540.

Programs

Mathematica

Table[Mod[n (n + 1)/2, DivisorSigma[1, n]], {n, 100}] (* T. D. Noe, Nov 27 2013 *)

Formula

a(n) = n(n+1)/2 mod A000203(n).