A163553 First differences of A024816.

0, 2, 1, 6, 0, 11, 1, 11, 5, 17, -4, 27, 4, 15, 9, 30, -3, 38, -2, 31, 18, 35, -12, 54, 15, 29, 12, 55, -12, 71, 1, 48, 28, 41, -7, 90, 16, 43, 6, 89, -12, 95, 4, 51, 52, 71, -28, 116, 14, 72, 26, 97, -12, 103, 8, 97, 48, 89, -48, 167, 28, 55, 41, 108, 6, 143, 10, 99, 22, 143

Offset: 1

Author

John W. Layman, Jul 30 2009

Keywords

• sign

Comments

A024816(n) is the sum of the non-divisors k of n for k=2,3,...,n-1.

It appears that (1) a(n) = A120444(n)+1 if and only if n is a prime, (2) if a(n)<0 then A120444(n)<0, and (3) a(n)<=0 whenever n is of the form 6k-1. Are these conjectures easy to prove/disprove? (A120444 is the first difference of A004125 Sum of remainders of n mod k, for k = 1,2,3,...,n).

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A004125, A024816, A120444.

Programs

Mathematica

Differences[Table[Total[Complement[Range[n],Divisors[n]]],{n,80}]] (* Harvey P. Dale, Mar 05 2013 *)

PARI

a(n) = n + 1 + sigma(n) - sigma(n+1); \\ Michel Marcus, Jul 29 2017