A219729 -id:A219729

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A219730

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

+10
3

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..56.

Steven Finch, 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) s2-14 (3): 521-526.

MATHEMATICA

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

CROSSREFS

Cf. A033677, A219729.

KEYWORD

nonn

AUTHOR

Michel Marcus, Nov 26 2012

STATUS

approved

A161416

Partial sums of A056737.

+10
0

0, 1, 3, 3, 7, 8, 14, 16, 16, 19, 29, 30, 42, 47, 49, 49, 65, 68, 86, 87, 91, 100, 122, 124, 124, 135, 141, 144, 172, 173, 203, 207, 215, 230, 232, 232, 268, 285, 295, 298, 338, 339, 381, 388, 392, 413, 459, 461, 461, 466, 480, 489, 541, 544, 550, 551, 567, 594

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

LINKS

Table of n, a(n) for n=1..58.

Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos

Omar E. Pol, Divisors and pi(x)

FORMULA

a(n) = A219730(n) - A219729(n). - Tamas Sandor Nagy, Jan 20 2024

CROSSREFS