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A100953
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Number of partitions of n into relatively prime parts such that multiplicities of parts are also relatively prime.
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62
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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
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OFFSET
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0,5
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LINKS
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FORMULA
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MAPLE
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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:
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MATHEMATICA
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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]}]];
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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