A087233 a(n) = floor(sigma(A002110(n))/A002110(n)); integer quotient of divisor-sum of primorial numbers and primorials.

1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6

Offset: 0

Author

Labos Elemer, Sep 01 2003

Keywords

• nonn
• easy

Links

• Amiram Eldar, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000203, A002110, A054640, A108775.

Programs

Mathematica

q[x_] := Apply[Times, Table[Prime[w], {w, 1, x}]]; q[0]=1; Table[Floor[DivisorSigma[1, a=q[u]]/q[u]//N], {u, 1, 300}]
seq[nmax_] := Floor[FoldList[Times, 1, 1 + 1/Prime[Range[nmax]]]]; seq[100] (* Amiram Eldar, Aug 10 2024 *)

PARI

a(n) = floor(vecprod(apply(x -> 1 + 1/x, primes(n)))); \\ Amiram Eldar, Aug 10 2024

Formula

From Amiram Eldar, Aug 10 2024: (Start)

a(n) = A108775(A002110(n)).

a(n) = floor(A054640(n)/A002110(n)).

a(n) = floor(Product_{k=1..n} (1 + 1/prime(k))). (End)

Extensions

Offset changed to 0 and a(0) prepended by Amiram Eldar, Aug 10 2024