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 A178480 For n=0,1,2,... list all products of the first n primes raised to some positive power not exceeding n. 3
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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.) LINKS EXAMPLE 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 ... PROG (PARI) for( L=0, 3, forvec( v=vector(L, i, [1, L]), print1( prod( j=1, L, prime(j)^v[L-j+1] )", "))) CROSSREFS Cf. A178483 Sequence in context: A036913 A117311 A125024 * A053660 A104969 A065005 Adjacent sequences:  A178477 A178478 A178479 * A178481 A178482 A178483 KEYWORD nonn AUTHOR M. F. Hasler, May 31 2010 STATUS approved

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