A072463 Shadow transform of sigma(n), A000203, starting with 0, sigma(1), sigma(2), ...

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, 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, 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

Offset

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Nicholas John Bizzell-Browning, LIE scales: Composing with scales of linear intervallic expansion, Ph. D. Thesis, Brunel Univ. (UK, 2024). See p. 39.

Lorenz Halbeisen and Norbert Hungerbuehler, Number theoretic aspects of a combinatorial function, Notes on Number Theory and Discrete Mathematics 5(4) (1999), 138-150; see Definition 7 for the shadow transform.

N. J. A. Sloane, Transforms.

Maple

s:= n-> `if`(n=0, 0, numtheory[sigma](n)):
a:= n-> add(`if`(modp(s(j), n)=0, 1, 0), j=0..n-1):
seq(a(n), n=0..120);  # Alois P. Heinz, Sep 16 2019

Crossrefs

Cf. A000203.

Sequence in context: A270747 A214517 A230594 * A128853 A136165 A134193

Adjacent sequences: A072460 A072461 A072462 * A072464 A072465 A072466

Keyword

nonn

Author

N. J. A. Sloane, Aug 02 2002

Status

approved