

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
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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_{de} 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] (* JeanFrançois Alcover, Dec 09 2017 *)


CROSSREFS

Sequence in context: A309108 A308056 A336965 * A333569 A110500 A161871
Adjacent sequences: A293300 A293301 A293302 * A293304 A293305 A293306


KEYWORD

nonn,mult


AUTHOR

R. J. Mathar, Oct 05 2017


STATUS

approved



