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 A329045 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(A329044(i)) = A046523(A329044(j)) for all i, j. 8
 1, 2, 2, 3, 2, 3, 2, 4, 4, 3, 2, 5, 2, 3, 6, 7, 2, 7, 2, 5, 6, 3, 2, 8, 9, 3, 4, 5, 2, 10, 2, 4, 6, 3, 11, 12, 2, 3, 6, 4, 2, 4, 2, 5, 10, 3, 2, 8, 13, 14, 6, 5, 2, 7, 9, 15, 6, 3, 2, 16, 2, 3, 16, 7, 17, 18, 2, 5, 6, 19, 2, 20, 2, 3, 21, 5, 22, 18, 2, 7, 13, 3, 2, 7, 23, 3, 6, 15, 2, 24, 25, 5, 6, 3, 26, 27, 2, 28, 24, 13, 2, 18, 2, 15, 29 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Restricted growth sequence transform of function f(n) = A046523(A329044(n)). For all i, j: A305800(i) = A305800(j) => a(i) = a(j), a(i) = a(j) => A324888(i) = A324888(j), a(i) = a(j) => A329046(i) = A329046(j). LINKS Antti Karttunen, Table of n, a(n) for n = 1..65537 PROG (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; }; A034386(n) = prod(i=1, primepi(n), prime(i)); A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A034386(f[i, 1])^f[i, 2]) }; \\ From A108951 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); }; A324886(n) = A276086(A108951(n)); A064989(n) = {my(f); f = factor(n); if((n>1 && f[1, 1]==2), f[1, 2] = 0); for (i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f)}; A329044(n) = A064989(A324886(n)); A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523 v329045 = rgs_transform(vector(up_to, n, A046523(A329044(n)))); A329045(n) = v329045[n]; CROSSREFS Cf. A034386, A064989, A108951, A276086, A305800, A324886, A324888, A329044, A329046. Cf. also A278226, A286626. Sequence in context: A308450 A229123 A173908 * A329345 A054030 A336311 Adjacent sequences: A329042 A329043 A329044 * A329046 A329047 A329048 KEYWORD nonn AUTHOR Antti Karttunen, Nov 08 2019 STATUS approved

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Last modified March 22 02:41 EDT 2023. Contains 361413 sequences. (Running on oeis4.)