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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). 7
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
Is abs(omega(a(n)) - omega(a(n+1))) <= 1? (Cf. A001221.) - David A. Corneth, Apr 16 2020
LINKS
David A. Corneth, Table of n, a(n) for n = 1..884 (terms 1..762 from Amiram Eldar, 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.
T. M. A. Fink, Number of ordered factorizations and recursive divisors, arXiv:2307.16691 [math.NT], 2023.
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. A001221, A001694, A002093, A033833, A074206, A163272, A330686 (after primorial deflation).
Sequence in context: A176777 A318761 A020153 * A338927 A286373 A286372
KEYWORD
nonn
AUTHOR
Amiram Eldar, May 02 2019
STATUS
approved

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Last modified June 17 03:50 EDT 2024. Contains 373432 sequences. (Running on oeis4.)