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1, 2, 2, 3, 2, 4, 2, 5, 6, 4, 2, 7, 2, 4, 4, 8, 2, 9, 2, 7, 4, 4, 2, 10, 11, 4, 12, 7, 2, 13, 2, 14, 4, 4, 4, 15, 2, 4, 4, 10, 2, 13, 2, 7, 9, 4, 2, 16, 17, 18, 4, 7, 2, 19, 4, 10, 4, 4, 2, 20, 2, 4, 9, 21, 4, 13, 2, 7, 4, 13, 2, 22, 2, 4, 18, 7, 4, 13, 2, 16, 23, 4, 2, 20, 4, 4, 4, 10, 2, 24, 4, 7, 4, 4, 4, 25, 2, 26, 9, 27, 2, 13, 2, 10, 13, 4, 2, 28, 2, 13
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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 A291757, which means that this is the lexicographically least sequence a, such that for all i, j: a(i) = a(j) <=> A291757(i) = A291757(j) <=> A003557(i) = A003557(j) and A046523(i) = A046523(j). That this is equal to the definition given in the title follows because any such lexicographically least sequence satisfying relation <=> is also the least sequence satisfying relation => with the same parameters.
Also the restricted growth sequence transform of A294876, Product_{d|n, d>1} prime(gcd(d,n/d)). (This was the original definition).
For all i, j:
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LINKS
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PROG
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(PARI)
up_to = 65537;
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; };
A294876(n) = { my(m=1); fordiv(n, d, if(d>1, m *= prime(gcd(d, n/d)))); m; };
v294877 = rgs_transform(vector(up_to, n, A294876(n)));
(PARI)
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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