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A257464
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Number of factorizations of m^n into 3 factors, where m is a product of exactly 3 distinct primes and each factor is a product of n primes (counted with multiplicity).
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2
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1, 1, 5, 10, 23, 40, 73, 114, 180, 262, 379, 521, 712, 938, 1228, 1567, 1986, 2469, 3052, 3715, 4499, 5383, 6410, 7558, 8875, 10335, 11991, 13816, 15865, 18110, 20611, 23336, 26350, 29620, 33213, 37095, 41338, 45904, 50870, 56197, 61964, 68131, 74782, 81873
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OFFSET
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0,3
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LINKS
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FORMULA
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G.f.: -(x^6-x^5+2*x^4+2*x^3+2*x^2-x+1)/((x^2+x+1)*(x+1)^2*(x-1)^5).
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EXAMPLE
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a(2) = 5: (2*3*5)^2 = 900 = 10*10*9 = 15*10*6 = 15*15*4 = 25*6*6 = 25*9*4.
a(4) = 23: (2*3*5)^4 = 810000 = 100*90*90 = 100*100*81 = 135*100*60 = 150*90*60 = 150*100*54 = 150*135*40 = 150*150*36 = 225*60*60 = 225*90*40 = 225*100*36 = 225*150*24 = 225*225*16 = 250*60*54 = 250*81*40 = 250*90*36 = 250*135*24 = 375*54*40 = 375*60*36 = 375*90*24 = 375*135*16 = 625*36*36 = 625*54*24 = 625*81*16.
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MAPLE
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a:= n-> coeff(series(-(x^6-x^5+2*x^4+2*x^3+2*x^2-x+1)/
((x^2+x+1)*(x+1)^2*(x-1)^5), x, n+1), x, n):
seq(a(n), n=0..60);
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MATHEMATICA
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CoefficientList[Series[-(x^6 - x^5 + 2 x^4 + 2 x^3 + 2 x^2 - x + 1)/((x^2 + x + 1) (x + 1)^2*(x - 1)^5), {x, 0, 43}], x] (* Michael De Vlieger, Jul 02 2018 *)
LinearRecurrence[{2, 1, -3, -1, 1, 3, -1, -2, 1}, {1, 1, 5, 10, 23, 40, 73, 114, 180}, 50] (* Harvey P. Dale, Jan 08 2022 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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