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A087980
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Numbers with strictly decreasing prime exponents.
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10
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1, 2, 4, 8, 12, 16, 24, 32, 48, 64, 72, 96, 128, 144, 192, 256, 288, 360, 384, 432, 512, 576, 720, 768, 864, 1024, 1152, 1440, 1536, 1728, 2048, 2160, 2304, 2592, 2880, 3072, 3456, 4096, 4320, 4608, 5184, 5760, 6144, 6912, 8192, 8640, 9216, 10368, 10800
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| This representation provides a natural ordering between strictly decreasing sequences of natural numbers. Let f and g be such sequences with f(1) > f(2) > ... > f(m) and g(1) > g(2) > ... > g(n). Define f < g iff p^f < p^g, where p^f is short for Product(i=1..m) p_i^f(i) and p^g is defined likewise as Product(i=1..n) p_i^g(i).
Note that "strictly decreasing sequences of natural numbers" is another way to say "partitions into distinct parts".
Also products of priomorial numbers p_1#^k_1 * p_2#^k_2 * ... * p_n#^k_n where all k_i > 0.
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
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FORMULA
| The numbers of the form Product(i=1..n) p_i^k_i where p_i = A000040(i) is the i-th prime and k_1 > k_2 > ... > k_n are positive natural numbers.
Compute x = 2^k_1 * 3^k_2 * 5^k_3 * 7^k_4 * 11^k_5 for k_1 > ... > k_5 allowing k_i = 0 for i > 1 and k_i = k_(i+1) in that case. Discard all x > 174636000 = 2^5*3^4*5^3*7^2*11 and enumerate those below. For more members take higher primes into account.
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EXAMPLE
| The sequence starts with a(1)=1, a(2)=2, a(3)=4 and a(4)=8. The next term is a(5)=12 = 2^2*3^1 = p_1^k_1 * p_2^k_2 with k_1=2 > k_2=1.
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CROSSREFS
| Cf. A000040, A025487, A002110, A000009.
Sequence in context: A070173 A116882 A069519 * A181818 A170892 A052184
Adjacent sequences: A087977 A087978 A087979 * A087981 A087982 A087983
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KEYWORD
| easy,nice,nonn
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AUTHOR
| Rainer Rosenthal (r.rosenthal(AT)web.de), Oct 27 2003
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EXTENSIONS
| Edited by Frank Adams-Watters (FrankTAW(AT)Netscape.net), Apr 25 2006
Offset change to 1 by T. D. Noe (noe(AT)sspectra.com), May 24 2010
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