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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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4
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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REFERENCES
| S. Ramanujan, A proof of Bertrand's postulate, J. Indian Math. Soc. 11 (1919), 181-182.
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
| S. Ramanujan, A Proof Of Bertrand's Postulate
V. Shevelev, Ramanujan and Labos primes, their generalizations and classifications of primes
J. Sondow, Ramanujan Prime in MathWorld
J. Sondow and E. W. Weisstein, Bertrand's Postulate in MathWorld
Wikipedia, Ramanujan prime
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FORMULA
| a(n)=Max{x; Pi[x]-Pi[x/2]=n}=Max{x; A056171(x)=n}=Man{x; A056169(n!)=n}; where Pi()=A000720().
a(n) = A104272(n+1) - 1 [From Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Aug 11 2008]
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EXAMPLE
| 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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CROSSREFS
| Cf. A056171, A056169, A000720, A000142, A080359.
Cf. A104272 Ramanujan primes.
Sequence in context: A155966 A104788 A036063 * A026320 A144206 A033460
Adjacent sequences: A080357 A080358 A080359 * A080361 A080362 A080363
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Feb 21 2003
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EXTENSIONS
| Definition corrected by Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Aug 10 2008
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