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A178479
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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.
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1
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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, 90, 100, 108, 120, 125, 135, 150, 180, 200, 216, 225, 250, 270, 300, 360, 375, 450, 500, 540, 600, 675, 750, 900, 1000, 1080, 1125, 1350, 1500, 1800, 2250, 2700, 3000, 3375
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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EXAMPLE
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n=0, n=1 and n=2 give a(1)=1 (empty product), a(2)=2=prime(1)^1,
and a(3..9) = 3, 4, 6, 9, 12, 18, 36: numbers 2^a 3^b with a,b <= 2.
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.
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PROG
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(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))) }
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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