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A336395
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Lexicographically earliest infinite sequence such that a(i) = a(j) => A278221(A000265(i)) = A278221(A000265(j)), for all i, j >= 1.
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2
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1, 1, 2, 1, 3, 2, 4, 1, 2, 3, 5, 2, 6, 4, 7, 1, 8, 2, 9, 3, 10, 5, 11, 2, 3, 6, 2, 4, 12, 7, 13, 1, 14, 8, 15, 2, 16, 9, 17, 3, 18, 10, 19, 5, 7, 11, 20, 2, 4, 3, 21, 6, 22, 2, 14, 4, 23, 12, 24, 7, 25, 13, 10, 1, 26, 14, 27, 8, 28, 15, 29, 2, 30, 16, 7, 9, 31, 17, 32, 3, 2, 18, 33, 10, 34, 19, 35, 5, 36, 7, 17, 11, 37, 20, 38, 2, 39, 4, 14, 3, 40, 21, 41, 6, 42
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OFFSET
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1,3
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COMMENTS
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Restricted growth sequence transform of the function f(n) = A278221(A000265(n)), the prime signature of the conjugated prime factorization of the odd part of n.
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; };
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
A122111(n) = if(1==n, n, my(f=factor(n), es=Vecrev(f[, 2]), is=concat(apply(primepi, Vecrev(f[, 1])), [0]), pri=0, m=1); for(i=1, #es, pri += es[i]; m *= prime(pri)^(is[i]-is[1+i])); (m));
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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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