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A098572
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a(n) = floor(Sum_{m=1..n} m^(1/m)).
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6
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1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) ~ n + log(n)^2/2 + c, where c = A363704 = sg1 + Sum_{k>=2} (-1)^k / k! * k-th derivative of zeta(k) = 0.9885496011422687506447541083399712644219986838..., where sg1 is the first Stieltjes constant (see A082633). - Vaclav Kotesovec, Jun 17 2023
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EXAMPLE
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floor(1^(1/1)+2^(1/2)+3^(1/3))=3 and floor(1^(1/1)+2^(1/2)+3^(1/3)+4^(1/4))=5.
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MAPLE
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option remember;
add(root[i](i), i=1..p) ;
floor(%) ;
end proc:
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MATHEMATICA
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Table[Floor[Sum[k^(1/k), {k, 1, n}]], {n, 1, 50}] (* G. C. Greubel, Feb 03 2018 *)
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PROG
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(PARI) for(n=1, 30, print1(floor(sum(k=1, n, k^(1/k))), ", ")) \\ G. C. Greubel, Feb 03 2018
(Magma) [Floor((&+[k^(1/k): k in [1..n]])): n in [1..30]]; // G. C. Greubel, Feb 03 2018
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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Mark Hudson (mrmarkhudson(AT)hotmail.com), Sep 16 2004
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STATUS
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approved
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