OFFSET
1,4
COMMENTS
For any given n >= 2, a(n)/(n-1) is the average of the |d(k)-d(k-1)| over all k with 2 <= k <= n.
Partial sums of |A051950|, i.e., a(n) = Sum_{i=2..n} |d(i)-d(i-1)| = Sum_{i=2..n} |A051950(i)|. - M. F. Hasler, Apr 21 2008
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..1000
FORMULA
The following is an empirical formula which is a very good fit for the range n >= 10290 out to about n = 500000000: a(n) ~= n*log(n)+(log(n)*0.122-1)*(n*log(log(n))). - Jack Brennen, Apr 21 2008. The constant 0.122 is an empirical guess analogous to Legendre's constant B in Pi(n) ~ n/(log(n)+B).
MATHEMATICA
nxt[{n_, a_}]:={n+1, a+Abs[DivisorSigma[0, n+1]-DivisorSigma[0, n]]}; NestList[ nxt, {1, 0}, 60][[All, 2]] (* Harvey P. Dale, Nov 05 2019 *)
PROG
(PARI) a(n)=sum(i=2, n, abs(numdiv(i)-numdiv(i-1))) \\ M. F. Hasler, Apr 21 2008
CROSSREFS
KEYWORD
nonn
AUTHOR
Leroy Quet, Apr 21 2008
EXTENSIONS
More terms from M. F. Hasler, Apr 21 2008
Edited by N. J. A. Sloane, Apr 26 2008
STATUS
approved