cp's OEIS Frontend

A178480 For n=0,1,2,... list all products of the first n primes raised to some positive power not exceeding n.

%I A178480 #5 Jan 08 2013 10:09:59
%S A178480 1,2,6,12,18,36,30,60,120,90,180,360,270,540,1080,150,300,600,450,900,
%T A178480 1800,1350,2700,5400,750,1500,3000,2250,4500,9000,6750,13500,27000,
%U A178480 210,420,840,1680,630,1260,2520,5040,1890,3780,7560,15120,5670,11340,22680
%N A178480 For n=0,1,2,... list all products of the first n primes raised to some positive power not exceeding n.
%C A178480 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.
%C A178480 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.)
%e A178480 The sequence begins: a(1)=1 (empty product); a(2)=2^1;
%e A178480 a(3,...,6)=2^1 3^1, 2^2 3^1, 2^1 3^2, 2^2 3^2;
%e A178480 a(7,...)=2^1 3^1 5^1, 2^2 3^1 5^1, 2^3 3^1 5^1,
%e A178480 ________ 2^1 3^2 5^1, 2^2 3^2 5^1, 2^3 3^2 5^1,
%e A178480 ________ 2^1 3^3 5^1, 2^2 3^3 5^1, 2^3 3^3 5^1,
%e A178480 ________ 2^1 3^1 5^2, 2^2 3^1 5^2, 2^3 3^1 5^2, ...
%e A178480 They correspond to the strings (cf. comment) "" a aa ab ba bb aaa aab aac aba abb abc aca acb acc baa bab bac ...
%o A178480 (PARI) for( L=0,3, forvec( v=vector(L,i,[1,L]), print1( prod( j=1,L,prime(j)^v[L-j+1] )",")))
%Y A178480 Cf. A178483
%K A178480 nonn
%O A178480 1,2
%A A178480 _M. F. Hasler_, May 31 2010