

A163553


First differences of A024816.


4



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
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OFFSET

1,2


COMMENTS

A024816(n) is the sum of the nondivisors k of n for k=2,3,...,n1.
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 6k1. 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



MATHEMATICA

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


PROG

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


CROSSREFS



KEYWORD

sign


AUTHOR



STATUS

approved



