

A219729


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


2



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
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OFFSET

1,2


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).  Michel Marcus, Nov 26 2012


LINKS

Ivan Neretin, Table of n, a(n) for n = 1..10000
S. Flinch, Multiples and divisors, January 27, 2004. [Cached copy, with permission of the author]
G. Tenenbaum, Sur deux fonctions de diviseurs, J. London Math. Soc. (1976) s214 (3): 521526.


MATHEMATICA

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


CROSSREFS

Cf. A033676, A219730.
Sequence in context: A102781 A139791 A027563 * A000534 A136112 A127936
Adjacent sequences: A219726 A219727 A219728 * A219730 A219731 A219732


KEYWORD

nonn


AUTHOR

Michel Marcus, Nov 26 2012


STATUS

approved



