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A128305
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a(n) is the smallest m such that g(m) is divisible by prime(n), where g is Landau's function A000793.
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4
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2, 3, 8, 14, 27, 32, 57, 62, 93, 118, 128, 178, 213, 215, 297, 346, 399, 429, 519, 510, 586, 687, 780, 920, 946, 1033, 1106, 1128, 1209, 1192, 1614, 1618, 1788, 1790, 1989, 1987, 2269, 2497, 2271, 2883, 2984, 2986, 3336, 3229, 3579, 3704, 4142, 4367, 4371
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OFFSET
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1,1
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LINKS
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EXAMPLE
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g(k) for k < 14 is not divisible by prime(4) = 7; g(14) = 84 = 7*12. Hence a(4) = 14.
g(k) for k < 32 is not divisible by prime(6) = 13; g(32) = 5460 = 13*420. Hence a(6) = 32.
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MATHEMATICA
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b[n_, i_] := b[n, i] = Module[{p}, p = If[i < 1, 1, Prime[i]]; If[n == 0 || i < 1, 1, Max[b[n, i - 1], Table[p^j*b[n - p^j, i - 1], {j, 1, Log[p, n] // Floor}]]]];
g[n_] := g[n] = b[n, If[n < 8, 3, PrimePi[Ceiling[1.328*Sqrt[n*Log[n] // Floor]]]]];
a[n_] := For[p = Prime[n]; m = 2, True, m++, If[Divisible[g[m], p], Print[n, " ", m]; Return[m]]];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Edited, a(6) inserted and a(12) to a(23) added by Klaus Brockhaus, May 07 2007
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STATUS
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approved
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