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%I #4 Jul 14 2012 11:32:33
%S 1,2,3,4,6,9,12,18,36,5,8,10,15,20,24,25,27,30,40,45,50,54,60,72,75,
%T 90,100,108,120,125,135,150,180,200,216,225,250,270,300,360,375,450,
%U 500,540,600,675,750,900,1000,1080,1125,1350,1500,1800,2250,2700,3000,3375
%N For n=0,1,2,... list all numbers not occurring earlier which can be written as product of the first n primes raised to some nonnegative power not exceeding n.
%C Every positive integer occurs exactly once in this sequence, but depending on its largest prime factor, it may appear quite late with respect to larger numbers. E.g. prime(4)=7=a(65) appears after a(4^3)=27000=(2*3*5)^3, prime(5)=11=a(626) appears after a(5^4)=(2*3*5*7)^4=1944810000.
%C First A000169(n) terms are the divisors of A181555(n), and a(A000169(n))=A181555(n). [From _Matthew Vandermast_, Oct 31 2010]
%e n=0, n=1 and n=2 give a(1)=1 (empty product), a(2)=2=prime(1)^1,
%e and a(3..9) = 3, 4, 6, 9, 12, 18, 36: numbers 2^a 3^b with a,b <= 2.
%e n=3 gives a(10..64) = 5, 8, 10, 12, 15, 18...: numbers 2^a 3^b 5^c not occurring earlier, with a,b,c <= 3.
%o (PARI) { s=[]; for( L=0,3, a=[]; forvec( v=vector(L,i,[0,L]), setsearch( s, t=prod( j=1,L,prime(j)^v[L-j+1] )) & next; s=setunion(s,Set(t)); a=concat(a,t)); apply(x->print1(x","),vecsort(a))) }
%Y Cf. A178480, A178483, A178484, A111791.
%K nonn
%O 1,2
%A _M. F. Hasler_, May 31 2010
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