OFFSET
1,4
COMMENTS
a(n) = 1''+2''+3''+4''+5''+...+n'' -> ~ constant * n^2 as n -> oo.
Note: a(n) = sum(D^d(i)^m,i=1..n) -> constant * n^(m+1) as n -> oo where D^d(i) is the derivative of order d th of the natural number i (results on arithmetic derivatives descent from Barbeau's paper in References).
LINKS
E. J. Barbeau, Remark on an arithmetic derivative, Canad. Math. Bull. vol. 4, no. 2, May 1961.
FORMULA
a(n) = sum(i'', i=1..n), where i'' is the second arithmetic derivative of i (A068346).
EXAMPLE
a(5) = 1'' + 2'' + 3'' + 4'' + 5'' = 0+0+0+4+0 = 4.
MAPLE
der:=n->n*add(op(2, p)/op(1, p), p=ifactors(n)[2]): seq(add(der(der(i)), i=1..j), j=1..55);
CROSSREFS
KEYWORD
nonn
AUTHOR
Giorgio Balzarotti, Nov 19 2013
STATUS
approved