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Smallest number with additive excess n.
0

%I #14 Feb 24 2022 02:54:32

%S 46,253,649,6049,69989,166213,551137,9064261,68444596,347562415,

%T 612220081

%N Smallest number with additive excess n.

%C Let m = Product p_j ^ a_j be the standard prime factorization of m. The additive excess of m is defined to be Sum||p_j ^ a_j|| - ||m|| where ||m||=A005245(n) is the complexity of n.

%C The n-th term of this sequence is the least number m with additive excess n.

%H J. Arias de Reyna and J. van de Lune, <a href="http://arxiv.org/abs/1404.1850">The question "How many 1's are needed?" revisited</a>, arXiv preprint arXiv:1404.1850 [math.NT], 2014.

%e ||253||=17, ||11||=8, ||23||=11. 11 + 8 - 17 = 2. The second term is 253.

%Y Cf. A244743, A005245.

%K nonn,more

%O 1,1

%A _Juan Arias-de-Reyna_, Jul 05 2014