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A054550
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Composite numbers whose least prime factor is either 5 or 7.
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1
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25, 35, 49, 55, 65, 77, 85, 91, 95, 115, 119, 125, 133, 145, 155, 161, 175, 185, 203, 205, 215, 217, 235, 245, 259, 265, 275, 287, 295, 301, 305, 325, 329, 335, 343, 355, 365, 371, 385, 395, 413, 415, 425, 427, 445, 455, 469, 475, 485, 497, 505, 511, 515, 535
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OFFSET
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1,1
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COMMENTS
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Original definition: Union of 4 AP's: 25+30n, 35+30n, 49+42n, 77+42n.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1).
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FORMULA
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G.f.: x*(25 + 10*x + 14*x^2 + 6*x^3 + 10*x^4 + 12*x^5 + 8*x^6 + 6*x^7 + 4*x^8 + 20*x^9 + 4*x^10 + 6*x^11 + 8*x^12 + 12*x^13 + 10*x^14 + 6*x^15 + 14*x^16 + 10*x^17 + 18*x^18 + 2*x^19 + 10*x^20 + 2*x^21 - 7*x^22) / ((1 - x)^2*(1 + x)*(1 - x + x^2 - x^3 + x^4 - x^5 + x^6 - x^7 + x^8 - x^9 + x^10)*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9 + x^10)). - Colin Barker, Nov 19 2018
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MATHEMATICA
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Union[Flatten[Table[{30n+{25, 35}, 42n+{49, 77}}, {n, 0, 20}]]] (* Harvey P. Dale, Feb 19 2016 *)
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PROG
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(PARI) select( is_A054550(n)=vecsum((n=factor(n, 0))[, 2])>1&&n[1, 1]>=5, [0..550]) \\ M. F. Hasler, Nov 18 2018
(PARI) Vec(x*(25 + 10*x + 14*x^2 + 6*x^3 + 10*x^4 + 12*x^5 + 8*x^6 + 6*x^7 + 4*x^8 + 20*x^9 + 4*x^10 + 6*x^11 + 8*x^12 + 12*x^13 + 10*x^14 + 6*x^15 + 14*x^16 + 10*x^17 + 18*x^18 + 2*x^19 + 10*x^20 + 2*x^21 - 7*x^22) / ((1 - x)^2*(1 + x)*(1 - x + x^2 - x^3 + x^4 - x^5 + x^6 - x^7 + x^8 - x^9 + x^10)*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9 + x^10)) + O(x^60)) \\ Colin Barker, Nov 19 2018
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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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Stuart M. Ellerstein (ellerstein(AT)aol.com), May 15 2000
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EXTENSIONS
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STATUS
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approved
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