A072453 Shadow transform of A000522.

0, 1, 1, 0, 1, 2, 0, 0, 1, 0, 2, 0, 0, 3, 0, 0, 1, 0, 0, 2, 2, 0, 0, 2, 0, 2, 3, 0, 0, 1, 0, 2, 1, 0, 0, 0, 0, 3, 2, 0, 2, 1, 0, 1, 0, 0, 2, 0, 0, 0, 2, 0, 3, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 1, 6, 0, 0, 0, 0, 0, 2, 0, 0, 3, 0, 2, 0, 0, 0, 2, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 4, 0, 1, 0, 0, 2, 0, 0, 1, 3

Offset

0,6

Links

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

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

OEIS Wiki, Shadow transform.

N. J. A. Sloane, Transforms.

Maple

A000522 := proc(n)
    add(n!/k!, k=0..n) ;
end proc:
shadD := proc(a)
    local s, n ;
    s := {} ;
    for n from 0 to a-1 do
        if A000522(n) mod a = 0 then
            s := s union {n} ;
        end if;
    end do:
    s ;
end proc:
A072453 := proc(a)
    nops(shadD(a)) ;
end proc: # R. J. Mathar, Jun 24 2013
# second Maple program:
b:= proc(n) option remember; n*b(n-1)+1 end: b(0):=1:
a:= n-> add(`if`(irem(b(j), n)=0, 1, 0), j=0..n-1):
seq(a(n), n=0..150);  # Alois P. Heinz, Jun 28 2018

Mathematica

b[n_] := b[n] = n*b[n - 1] + 1 ; b[0] = 1;
a[n_] := Sum[If[Mod[b[j], n] == 0, 1, 0], {j, 0, n - 1}];
a /@ Range[0, 104] (* Jean-François Alcover, Jan 15 2020, after Alois P. Heinz *)

Crossrefs

Cf. A000522, A072456.

Sequence in context: A129448 A239003 A123759 * A307303 A324252 A321445

Adjacent sequences: A072450 A072451 A072452 * A072454 A072455 A072456

Keyword

nonn,mult,easy

Author

N. J. A. Sloane, Aug 02 2002

Extensions

More terms from Christian G. Bower, Jun 08 2005

Status

approved