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A087233
a(n) = floor(sigma(A002110(n))/A002110(n)); integer quotient of divisor-sum of primorial numbers and primorials.
1
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
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
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