A200726 - OEIS

A200726

Define a map f from primes to integers mod 4 by f(p) = 0,1,3,2,1 according as p == 1,2,3,4,0 mod 5; a(n) = Sum_{all primes p} v_p(n)*f(p), where v_p(n) is the exponent of the highest power of p dividing n.

0, 1, 3, 2, 1, 0, 1, 3, 2, 2, 0, 1, 3, 2, 0, 0, 1, 3, 2, 3, 0, 1, 3, 2, 2, 0, 1, 3, 2, 1, 0, 1, 3, 2, 2, 0, 1, 3, 2, 0, 0, 1, 3, 2, 3, 0, 1, 3, 2, 3, 0, 1, 3, 2, 1, 0, 1, 3, 2, 2, 0, 1, 3, 2, 0, 0, 1, 3, 2, 3, 0, 1, 3, 2, 1, 0, 1, 3, 2, 1, 0, 1, 3, 2, 2, 0, 1, 3, 2

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OFFSET

1,3

COMMENTS

All calculations are done mod 4.

LINKS

Table of n, a(n) for n=1..89.

Dimitri Hendriks, Frits G. W. Dannenberg, Jorg Endrullis, Mark Dow and Jan Willem Klop, Arithmetic Self-Similarity of Infinite Sequences, arXiv preprint 1201.3786 [math.CO], 2012.

EXAMPLE

n=4: v_2(4)=2, v_p(4)=0 for p>2, so a(4)=2*f(2)=2*1=2.

MAPLE

with(padic) ;

A200726f := proc(p)

op(1+(p mod 5), [1, 0, 1, 3, 2]) ;

end proc:

A200726 := proc(n)

local a, e;

a := 0 ;

for e in ifactors(n)[2] do

p := op(1, e) ;

a := a+ ordp(n, p)*A200726f(p) ;

end do:

return (a mod 4 );

end proc:

seq(A200726(n), n=1..90) ; # R. J. Mathar, Jun 28 2012

MATHEMATICA

f[p_] := {1, 0, 1, 3, 2}[[Mod[p, 5] + 1]];

a[1] = 0; a[n_] := Sum[IntegerExponent[n, p]*f[p], {p, FactorInteger[n][[ All, 1]]}] // Mod[#, 4]&;

Array[a, 90] (* Jean-François Alcover, Nov 29 2017 *)

CROSSREFS

Sequence in context: A291760 A291759 A068494 * A195040 A250486 A316826

Adjacent sequences: A200723 A200724 A200725 * A200727 A200728 A200729

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, May 06 2012

STATUS

approved