A219729 Sum_{x <= n} largest divisor of x that is <= sqrt(x).

1, 2, 3, 5, 6, 8, 9, 11, 14, 16, 17, 20, 21, 23, 26, 30, 31, 34, 35, 39, 42, 44, 45, 49, 54, 56, 59, 63, 64, 69, 70, 74, 77, 79, 84, 90, 91, 93, 96, 101, 102, 108, 109, 113, 118, 120, 121, 127, 134, 139, 142, 146, 147, 153, 158, 165, 168, 170, 171, 177, 178

Offset: 1

Author

Michel Marcus, Nov 26 2012

Keywords

• nonn

Comments

G. Tenenbaum proved that limit(log(a(n)/n^(3/2)))/log(log(n)) is -b with b = 1-(1+loglog 2)/log 2 = 0.08607... (same constant as in A027424 comment) (théorème 1).

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000
• Steven Finch, Multiples and divisors, January 27, 2004. [Cached copy, with permission of the author]
• Gérald Tenenbaum, Sur deux fonctions de diviseurs, J. London Math. Soc. (1976) s2-14 (3): 521-526; alternative copy.

Crossrefs

Cf. A027424, A033676, A219730.

Programs

Mathematica

t = Table[d = Divisors[n]; d[[Ceiling[Length[d]/2]]], {n, 100}]; Accumulate[t] (* T. D. Noe, Nov 26 2012 *)