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Search: id:A080360
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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; listen)
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OFFSET
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1,1
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REFERENCES
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S. Ramanujan, A proof of Bertrand's postulate, J. Indian Math. Soc. 11 (1919), 181-182. [From Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Aug 11 2008]
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.. [From Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Aug 11 2008]
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LINKS
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S. Ramanujan, A Proof Of Bertrand's Postulate [From Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Aug 11 2008]
J. Sondow, Ramanujan Prime in MathWorld [From Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Aug 10 2008]
J. Sondow and E. W. Weisstein, Bertrand's Postulate in MathWorld [From Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Aug 11 2008]
Wikipedia, Ramanujan prime [From Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Aug 11 2008]
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FORMULA
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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
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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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CROSSREFS
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Cf. A056171, A056169, A000720, A000142, A080359.
Cf. A104272 Ramanujan primes. [From Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Aug 10 2008]
Sequence in context: A155966 A104788 A036063 this_sequence A026320 A144206 A033460
Adjacent sequences: A080357 A080358 A080359 this_sequence A080361 A080362 A080363
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Feb 21 2003
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EXTENSIONS
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Definition corrected by Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Aug 10 2008
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