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A307866 K-champion numbers: numbers m such that K(m) > K(j) for all j < m, where K(m) is the Kalmár function (A074206). 4
0, 1, 4, 6, 8, 12, 24, 36, 48, 72, 96, 120, 144, 192, 240, 288, 360, 432, 480, 576, 720, 864, 960, 1152, 1440, 1728, 1920, 2160, 2304, 2880, 3456, 4320, 5760, 6912, 8640, 11520, 17280, 23040, 25920, 30240, 34560, 46080, 51840, 60480, 69120, 86400, 103680, 120960 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

The corresponding record values are 0, 1, 2, 3, 4, 8, 20, 26, 48, 76, 112, 132, 208, ... (see the link for more values).

Deléglise et al. (2008) proved that the number of powerful (A001694) terms in this sequence is finite. They ask whether a(391) = 485432135516160000 (the 112th powerful term) is the largest. - Amiram Eldar, Aug 20 2019

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..762, calculated by Deléglise et al.

M. Deléglise, M. O. Hernane, and J.-L. Nicolas, Grandes valeurs et nombres champions de la fonction arithmétique de Kalmár, Journal of Number Theory, Vol. 128, No. 6 (2008), pp. 1676-1716.

M. Deléglise, M. O. Hernane, and J.-L. Nicolas, Tables des 761 premiers champions de la fonction de Kalmar, alternative link.

Amiram Eldar, Table of n, a(n), A074206(a(n)), calculated by Deléglise et al.

FORMULA

For n >= 1, a(1+n) = A108951(A330686(n)). - Antti Karttunen, Dec 31 2019

MATHEMATICA

a[0] = 0; a[1] = 1; a[n_] := a[n] = Total[a /@ Most[Divisors[n]]]; s = {}; am=-1; Do[a1 = a[n]; If[a1>am, am=a1; AppendTo[s, n]], {n, 0, 10000}]; s

CROSSREFS

Cf. A001694, A002093, A033833, A074206, A163272, A330686 (after primorial deflation).

Sequence in context: A176777 A318761 A020153 * A286373 A286372 A151760

Adjacent sequences:  A307863 A307864 A307865 * A307867 A307868 A307869

KEYWORD

nonn

AUTHOR

Amiram Eldar, May 02 2019

STATUS

approved

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Last modified February 28 08:28 EST 2020. Contains 332323 sequences. (Running on oeis4.)