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A123201
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Numbers m such that the factorizations of m..m+7 have the same number of primes (including multiplicities).
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12
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3405122, 3405123, 6612470, 8360103, 8520321, 9306710, 10762407, 12788342, 12788343, 15212151, 15531110, 16890901, 17521382, 17521383, 21991382, 21991383, 22715270, 22715271, 22841702, 22841703, 22914722, 22914723
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OFFSET
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1,1
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COMMENTS
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Note that because 3405130 = 2*5*167*2039 is also the product of 4 primes, 3405122 is the first m such that numbers m..m+8 are products of the same number k of primes (k=4).
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LINKS
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EXAMPLE
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3405122 = 2*7*29*8387, 3405123 = 3^2*19*19913, 3405124 = 2^2*127*6703, 3405125 = 5^3*27241, 3405126 = 2*3*59*9619, 3405127 = 11*23*43*313, 3405128 = 2^3*425641, 3405129 = 3*7*13*12473 all products of 4 primes.
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PROG
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(PARI) c=0; p1=0; for(n=2, 10^8, p2=bigomega(n); if(p1==p2, c++; if(c>=7, print1(n-7 ", ")), c=0; p1=p2)) \\ Donovan Johnson, Mar 20 2013
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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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