A013940 a(n) = Sum_{k=1..n} floor(n/prime(k)^2).

0, 0, 0, 1, 1, 1, 1, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 6, 6, 7, 7, 7, 7, 8, 9, 9, 10, 11, 11, 11, 11, 12, 12, 12, 12, 14, 14, 14, 14, 15, 15, 15, 15, 16, 17, 17, 17, 18, 19, 20, 20, 21, 21, 22, 22, 23, 23, 23, 23, 24, 24, 24, 25, 26, 26, 26, 26, 27, 27, 27, 27, 29

Offset: 1

Author

N. J. A. Sloane, Henri Lifchitz, Dec 11 1996

Keywords

• nonn

Comments

Partial sums of A056170. - Michel Marcus, Aug 24 2013

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A085548.

Programs

Magma

[(&+[Floor(n/NthPrime(k)^2): k in [1..n]]): n in [1..70]]; // G. C. Greubel, Nov 25 2018

Maple

A056170:= n -> nops(select(t -> (t[2]>1), ifactors(n)[2]));
N:= 10000; # to get terms up to a(N)
A:= map(round,Statistics:-CumulativeSum(Array(1..N, A056170)));
seq(A[n],n=1..N); # Robert Israel, Jun 03 2014

Mathematica

Table[Sum[Floor[n/Prime[k]^2],{k,n}],{n,70}] (* Harvey P. Dale, Mar 30 2018 *)

PARI

a(n) = sum(k = 1, n, n\prime(k)^2); \\ Michel Marcus, Aug 24 2013

PARI

a(n) = my(s=0); forprime(p=2, sqrtint(n), s += n\(p*p)); s; \\ Daniel Suteu, Nov 24 2018

Sage

[sum(floor(n/nth_prime(k)^2) for k in (1..n)) for n in (1..70)] # G. C. Greubel, Nov 25 2018

Formula

G.f.: (1/(1 - x))*Sum_{k>=1} x^(prime(k)^2)/(1 - x^(prime(k)^2)). - Ilya Gutkovskiy, Feb 11 2017

a(n) ~ A085548 * n. - Daniel Suteu, Nov 24 2018