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A293303 Exponential convolution of the exponential Mobius function and the natural numbers. 1
1, 2, 3, 2, 5, 6, 7, 6, 6, 10, 11, 6, 13, 14, 15, 12, 17, 12, 19, 10, 21, 22, 23, 18, 20, 26, 24, 14, 29, 30, 31, 30, 33, 34, 35, 12, 37, 38, 39, 30, 41, 42, 43, 22, 30, 46, 47, 36, 42, 40, 51, 26, 53, 48, 55, 42, 57, 58, 59, 30, 61, 62, 42, 54, 65, 66, 67 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Exponential convolution of A166234 and A000027.

Similar to the definition of A000010 as the Dirichlet convolution of A008683 and A000027.

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

A. V. Lelechnko, Exponenital and infinitary divisors, arXiv:1405.7597, sequence f^E(n).

FORMULA

Multiplicative with a(p^e) = Sum_{d|e} A008683(e/d)*p^d.

MAPLE

A293303 := proc(n)

    local a, pe, i, p, e, f, d ;

    a := 1 ;

    for pe in ifactors(n)[2] do

        p := pe[1] ;

        e := pe[2] ;

        f := 0 ;

        for d in numtheory[divisors](e) do

            f := f+numtheory[mobius](e/d)*p^d ;

        end do:

        a := a*f ;

    end do:

    a ;

end proc:

seq(A293303(n), n=1..100) ;

MATHEMATICA

s[p_, e_] := DivisorSum[e, MoebiusMu[e/#]*p^#&];

a[n_] := a[n] = Times @@ s @@@ FactorInteger[n];

Array[a, 100] (* Jean-François Alcover, Dec 09 2017 *)

CROSSREFS

Sequence in context: A186646 A309108 A308056 * A110500 A161871 A135875

Adjacent sequences:  A293300 A293301 A293302 * A293304 A293305 A293306

KEYWORD

nonn,mult,changed

AUTHOR

R. J. Mathar, Oct 05 2017

STATUS

approved

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Last modified September 18 10:13 EDT 2019. Contains 327170 sequences. (Running on oeis4.)