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A080360
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a(n) is the largest positive integer x such that the number of unitary-prime-divisors of x! equals n. Same as the largest positive integer x such that the number of primes in (x/2,x] equals n.
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6
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10, 16, 28, 40, 46, 58, 66, 70, 96, 100, 106, 126, 148, 150, 166, 178, 180, 226, 228, 232, 238, 240, 262, 268, 280, 306, 310, 346, 348, 366, 372, 400, 408, 418, 430, 432, 438, 460, 486, 490, 502, 568, 570, 586, 592, 598, 600, 606, 640, 642, 646, 652, 658, 676
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OFFSET
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1,1
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REFERENCES
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S. Ramanujan, Collected Papers of Srinivasa Ramanujan (Ed. G. H. Hardy, S. Aiyar, P. Venkatesvara and B. M. Wilson), Amer. Math. Soc., Providence, 2000, pp. 208-209.
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LINKS
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FORMULA
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EXAMPLE
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n=5: in 46! five unitary-prime-divisors[UPD] appear: {29,31,37,41,43}. In larger factorials number of UPD is not more equal 5. Thus a(5)=46.
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MATHEMATICA
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nn = 60; R = Table[0, {nn}]; s = 0;
Do[If[PrimeQ[k], s++]; If[PrimeQ[k/2], s--]; If[s < nn, R[[s+1]] = k], {k, Prime[3*nn]}];
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CROSSREFS
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KEYWORD
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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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