OFFSET
0,5
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..10000
FORMULA
Moebius transform of A000837.
MAPLE
read transforms : a000837 := [] : b000837 := fopen("b000837.txt", READ) : bfil := readline(b000837) : while StringTools[WordCount](bfil) > 0 do b := sscanf( bfil, "%d %d") ; a000837 := [op(a000837), op(2, b)] ; bfil := readline(b000837) ; od: fclose(b000837) ; a000837 := subsop(1=NULL, a000837) : a := MOBIUS(a000837) : for n from 1 to 120 do printf("%d, ", op(n, a)) ; od: # R. J. Mathar, Mar 12 2008
# second Maple program:
with(numtheory): with(combinat):
b:= proc(n) option remember; `if`(n=0, 1, add(
mobius(n/d)*numbpart(d), d=divisors(n)))
end:
a:= proc(n) option remember; `if`(n=0, 1, add(
mobius(n/d)*b(d), d=divisors(n)))
end:
seq(a(n), n=0..60); # Alois P. Heinz, Dec 19 2017
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], And[GCD@@#===1, GCD@@Length/@Split[#]===1]&]], {n, 20}] (* Gus Wiseman, Dec 19 2017 *)
b[n_] := b[n] = If[n==0, 1, Sum[
MoebiusMu[n/d]*PartitionsP[d], {d, Divisors[n]}]];
a[n_] := a[n] = If[n==0, 1, Sum[
MoebiusMu[n/d]*b[d], {d, Divisors[n]}]];
a /@ Range[0, 60] (* Jean-François Alcover, May 21 2021, after Alois P. Heinz *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Jan 11 2005
EXTENSIONS
More terms from David Wasserman and R. J. Mathar, Mar 04 2008
a(0)=1 prepended by Alois P. Heinz, Dec 19 2017
STATUS
approved