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A300226
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Filter sequence combining A046523(n) and A052126(n), the prime signature of n and n/(largest prime dividing n).
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16
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1, 2, 2, 3, 2, 4, 2, 5, 6, 4, 2, 7, 2, 4, 8, 9, 2, 10, 2, 7, 8, 4, 2, 11, 12, 4, 13, 7, 2, 14, 2, 15, 8, 4, 16, 17, 2, 4, 8, 11, 2, 14, 2, 7, 18, 4, 2, 19, 20, 21, 8, 7, 2, 22, 16, 11, 8, 4, 2, 23, 2, 4, 18, 24, 16, 14, 2, 7, 8, 25, 2, 26, 2, 4, 27, 7, 28, 14, 2, 19, 29, 4, 2, 23, 16, 4, 8, 11, 2, 30, 28, 7, 8, 4, 16, 31, 2, 32, 18, 33, 2, 14, 2, 11, 34
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OFFSET
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1,2
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COMMENTS
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Restricted growth sequence transform of P(A046523(n), A052126(n)), where P(a,b) is a two-argument form of A000027 used as a Cantor pairing function N x N -> N.
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LINKS
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EXAMPLE
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a(6) = a(10) (= 4) because both are nonsquare semiprimes (2*3 and 2*5), and when the largest prime factor is divided out, both yield the same quotient, 2.
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PROG
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(PARI)
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om, invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om, invec[i], i); outvec[i] = u; u++ )); outvec; };
write_to_bfile(start_offset, vec, bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
A052126(n) = if(1==n, n, my(f=factor(n)[, 1], gpf = f[#f]); n/gpf); \\ After code in A052126.
write_to_bfile(1, rgs_transform(vector(65537, n, Aux300226(n))), "b300226.txt");
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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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