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

0,3

Links

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

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)

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 *)

Prog

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

Crossrefs

Cf. A000203, A002110, A054640, A108775.

Sequence in context: A342882 A025423 A284263 * A104147 A227568 A232746

Adjacent sequences: A087230 A087231 A087232 * A087234 A087235 A087236

Keyword

nonn,easy

Author

Labos Elemer, Sep 01 2003

Extensions

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

Status

approved