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A100953 Number of partitions of n into relatively prime parts such that multiplicities of parts are also relatively prime. 62
1, 1, 0, 1, 2, 5, 5, 13, 14, 25, 28, 54, 54, 99, 105, 160, 192, 295, 315, 488, 546, 760, 890, 1253, 1404, 1945, 2234, 2953, 3459, 4563, 5186, 6840, 7909, 10029, 11716, 14843, 17123, 21635, 25035, 30981, 36098, 44581, 51370, 63259, 73223, 88739, 103048, 124752 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,5
LINKS
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
Sequence in context: A183719 A239340 A124201 * A112835 A206625 A176168
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

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)