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A328628
Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(A328624(i)) = A046523(A328624(j)) for all i, j.
5
1, 2, 2, 3, 4, 5, 2, 5, 3, 6, 7, 8, 4, 3, 9, 10, 3, 11, 12, 13, 5, 14, 15, 16, 17, 9, 13, 18, 19, 14, 2, 5, 5, 14, 3, 11, 3, 14, 6, 20, 21, 22, 7, 18, 23, 24, 18, 25, 26, 23, 16, 27, 28, 29, 30, 31, 32, 33, 34, 35, 4, 3, 3, 6, 19, 14, 9, 16, 10, 36, 37, 38, 39, 40, 41, 42, 40, 43, 13, 8, 11, 44, 10, 45, 26, 23, 46, 47, 21, 22, 12, 13, 13, 18, 7, 8, 48, 49, 40
OFFSET
0,2
COMMENTS
Restricted growth sequence transform of function f(n) = A046523(A328624(n)) = A278226(A328625(n)).
For all i, j:
a(i) = a(j) => A328630(i) = A328630(j).
The scatter plot looks like a mound (or hive) of insects. - Antti Karttunen, Jan 09 2023
PROG
(PARI)
up_to = 32768;
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
A328624(n) = { my(m=1, p=2, e, g=1); while(n, e = (n%p); m *= (p^((g*e)%p)); g = e+1; n = n\p; p = nextprime(1+p)); (m); };
Aux328628(n) = A046523(A328624(n));
v328628 = rgs_transform(vector(1+up_to, n, Aux328628(n-1)));
A328628(n) = v328628[1+n];
CROSSREFS
KEYWORD
nonn,look
AUTHOR
Antti Karttunen, Oct 25 2019
STATUS
approved