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A178480
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For n=0,1,2,... list all products of the first n primes raised to some positive power not exceeding n.
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3
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1, 2, 6, 12, 18, 36, 30, 60, 120, 90, 180, 360, 270, 540, 1080, 150, 300, 600, 450, 900, 1800, 1350, 2700, 5400, 750, 1500, 3000, 2250, 4500, 9000, 6750, 13500, 27000, 210, 420, 840, 1680, 630, 1260, 2520, 5040, 1890, 3780, 7560, 15120, 5670, 11340, 22680
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OFFSET
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1,2
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COMMENTS
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Alternate construction: For n=0,1,2,... write all strings of length n using the first n symbols of the alphabet (""; a; aa,ab,ba,bb; aaa,aab,aac, aba,...), then code / interpret them as "positional" notation of exponents (a=1, b=2, ...) of primes (last digit = least prime), e.g.: acb => [1,3,2] => 5^1 3^3 2^2.
These numbers have the property that, if a prime p divides the number, then all primes less than p also divide it. (But not all such numbers are listed, neither are they listed in increasing order.)
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LINKS
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Table of n, a(n) for n=1..48.
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EXAMPLE
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The sequence begins: a(1)=1 (empty product); a(2)=2^1;
a(3,...,6)=2^1 3^1, 2^2 3^1, 2^1 3^2, 2^2 3^2;
a(7,...)=2^1 3^1 5^1, 2^2 3^1 5^1, 2^3 3^1 5^1,
________ 2^1 3^2 5^1, 2^2 3^2 5^1, 2^3 3^2 5^1,
________ 2^1 3^3 5^1, 2^2 3^3 5^1, 2^3 3^3 5^1,
________ 2^1 3^1 5^2, 2^2 3^1 5^2, 2^3 3^1 5^2, ...
They correspond to the strings (cf. comment) "" a aa ab ba bb aaa aab aac aba abb abc aca acb acc baa bab bac ...
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PROG
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(PARI) for( L=0, 3, forvec( v=vector(L, i, [1, L]), print1( prod( j=1, L, prime(j)^v[L-j+1] )", ")))
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CROSSREFS
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Cf. A178483
Sequence in context: A036913 A117311 A125024 * A053660 A104969 A065005
Adjacent sequences: A178477 A178478 A178479 * A178481 A178482 A178483
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KEYWORD
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nonn
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AUTHOR
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M. F. Hasler, May 31 2010
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STATUS
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approved
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