A098572 a(n) = floor(Sum_{m=1..n} m^(1/m)).

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

Offset: 1

Author

Mark Hudson (mrmarkhudson(AT)hotmail.com), Sep 16 2004

Keywords

• easy
• nonn

Examples

			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.
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..10000 (terms 1..5000 from G. C. Greubel)

Crossrefs

Cf. A351885, A363704.

Programs

Magma

[Floor((&+[k^(1/k): k in [1..n]])): n in [1..30]]; // G. C. Greubel, Feb 03 2018

Maple

A098572 := proc(p)
    option remember;
    add(root[i](i),i=1..p) ;
    floor(%) ;
end proc:

Mathematica

Table[Floor[Sum[k^(1/k), {k, 1, n}]], {n, 1, 50}] (* G. C. Greubel, Feb 03 2018 *)

PARI

for(n=1,30, print1(floor(sum(k=1,n, k^(1/k))), ", ")) \\ G. C. Greubel, Feb 03 2018

Formula

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