A219730 Sum_{x <= n} smallest divisor of x that is >= sqrt(x).

1, 3, 6, 8, 13, 16, 23, 27, 30, 35, 46, 50, 63, 70, 75, 79, 96, 102, 121, 126, 133, 144, 167, 173, 178, 191, 200, 207, 236, 242, 273, 281, 292, 309, 316, 322, 359, 378, 391, 399, 440, 447, 490, 501, 510, 533, 580, 588, 595, 605, 622, 635, 688, 697, 708, 716

Offset: 1

Author

Michel Marcus, Nov 26 2012

Keywords

• nonn

Comments

G. Tenenbaum proved that a(n) is asymptotically equal to (Pi^2/12)*n^2/log(n) (Théorème 2).

Links

• Robert Israel, 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. A033677, A219729.

Programs

Maple

g:= proc(n) min(select(t -> t^2 >= n, numtheory:-divisors(n))) end proc:
ListTools:-PartialSums(map(g, [$1..100])); # Robert Israel, Nov 22 2024

Mathematica

Accumulate[Table[First[Select[Divisors[n],#>=Sqrt[n]&]],{n,56}]] (* James C. McMahon, Jun 18 2024 *)