A092494 a(n) = Sum_{p prime and p<=n} ceiling(n/p).

0, 1, 3, 4, 6, 7, 10, 11, 12, 13, 16, 17, 20, 21, 23, 25, 27, 28, 31, 32, 34, 36, 39, 40, 42, 43, 45, 46, 49, 50, 54, 55, 56, 58, 60, 62, 65, 66, 68, 70, 73, 74, 78, 79, 81, 83, 86, 87, 89, 90, 92, 94, 97, 98, 100, 102, 104, 106, 109, 110, 114, 115, 117, 119, 120, 122

Offset: 1

Author

Reinhard Zumkeller, Apr 05 2004

Keywords

• nonn

Comments

a(n) = A013939(n) + A048865(n).

Links

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

Crossrefs

Cf. A006590.

Programs

Maple

N:= 100: # for a(1)..a(N)
V:= Vector(N):
p:= 0:
do
  p:= nextprime(p);
  if p > N then break fi;
  V[p]:= V[p]+1;
  for k from 2 to floor(N/p) do
    V[(k-1)*p+1 .. k*p]:= V[(k-1)*p+1 .. k*p] +~ k;
  od;
  if (k-1)*p+1<=N then V[(k-1)*p+1..N]:= V[(k-1)*p+1..N]+~ k fi
od:
convert(V,list); # Robert Israel, Jun 19 2019

PARI

a(n) = sum(k=1, n, isprime(k)*ceil(n/k)); \\ Michel Marcus, Jun 19 2019