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A248777 Greatest k such that k^8 divides n! 3
1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 24, 24, 24, 24, 24, 24, 48, 240, 720, 720, 720, 720, 720, 720, 720, 720, 1440, 1440, 1440, 1440, 1440, 10080, 10080, 10080, 20160, 20160, 60480, 60480, 60480, 60480 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,10
COMMENTS
Every term divides all its successors.
LINKS
EXAMPLE
a(10) = 2 because 2^10 divides 8! and if k > 2 then k^8 does not divide 8!.
MATHEMATICA
z = 60; f[n_] := f[n] = FactorInteger[n!]; r[m_, x_] := r[m, x] = m*Floor[x/m];
u[n_] := Table[f[n][[i, 1]], {i, 1, Length[f[n]]}];
v[n_] := Table[f[n][[i, 2]], {i, 1, Length[f[n]]}];
p[m_, n_] := p[m, n] = Product[u[n][[i]]^r[m, v[n]][[i]], {i, 1, Length[f[n]]}];
m = 8; Table[p[m, n], {n, 1, z}] (* A248776 *)
Table[p[m, n]^(1/m), {n, 1, z}] (* A248777 *)
Table[n!/p[m, n], {n, 1, z}] (* A248778 *)
CROSSREFS
Sequence in context: A330487 A339169 A171818 * A175101 A001991 A305706
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Oct 14 2014
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)