A072463 - OEIS

%I #16 Oct 23 2024 11:51:35

%S 0,1,1,2,2,1,2,2,2,1,1,1,3,2,3,2,1,1,3,1,2,2,1,1,4,1,1,1,2,1,3,3,3,1,

%T 1,1,3,1,2,2,2,1,4,1,2,2,1,1,5,1,1,1,1,1,3,1,3,2,1,1,6,1,3,2,1,1,1,1,

%U 2,1,1,1,8,1,2,1,1,1,2,1,3,1,1,1,6,1,1,1,1,1,5,2,1,3,1,1,5,1,3,1,1,1,2,1,3

%N Shadow transform of sigma(n), A000203, starting with 0, sigma(1), sigma(2), ...

%H Alois P. Heinz, <a href="/A072463/b072463.txt">Table of n, a(n) for n = 0..10000</a>

%H Nicholas John Bizzell-Browning, <a href="https://bura.brunel.ac.uk/handle/2438/29960">LIE scales: Composing with scales of linear intervallic expansion</a>, Ph. D. Thesis, Brunel Univ. (UK, 2024). See p. 39.

%H Lorenz Halbeisen and Norbert Hungerbuehler, <a href="https://www.semanticscholar.org/paper/Number-theoretic-aspects-of-a-combinatorial-Halbeisen-Hungerb%C3%BChler/5743ff2f9c14d22d1a9e570d6951a7c9ef79a612">Number theoretic aspects of a combinatorial function</a>, Notes on Number Theory and Discrete Mathematics 5(4) (1999), 138-150; see Definition 7 for the shadow transform.

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>.

%p s:= n-> `if`(n=0, 0, numtheory[sigma](n)):

%p a:= n-> add(`if`(modp(s(j), n)=0, 1, 0), j=0..n-1):

%p seq(a(n), n=0..120);  # _Alois P. Heinz_, Sep 16 2019

%Y Cf. A000203.

%K nonn

%O 0,4

%A _N. J. A. Sloane_, Aug 02 2002