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A350064
Lexicographically earliest infinite sequence such that a(i) = a(j) => A350062(i) = A350062(j), for all i, j >= 1.
5
1, 2, 3, 3, 4, 3, 5, 3, 6, 4, 7, 3, 8, 3, 6, 6, 9, 3, 10, 3, 11, 6, 12, 3, 11, 6, 6, 6, 13, 6, 14, 3, 6, 6, 11, 5, 15, 3, 16, 6, 17, 3, 18, 3, 6, 19, 20, 3, 19, 4, 16, 3, 21, 3, 22, 3, 16, 11, 23, 3, 24, 6, 6, 11, 11, 6, 25, 6, 6, 3, 26, 6, 27, 6, 6, 6, 19, 6, 28, 3, 16, 6, 29, 11, 30, 16, 31, 19, 32, 11, 33, 6, 30, 30, 30
OFFSET
1,2
COMMENTS
Restricted growth sequence transform of A350062.
For all i, j >= 1: a(i) = a(j) => A324105(i) = A324105(j).
For all i, j >= 2:
a(i) = a(j) => A324119(i) = A324119(j),
a(i) = a(j) => A342655(i) = A342655(j).
PROG
(PARI)
up_to = 3000;
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
A156552(n) = { my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res };
A350062(n) = if(1==n, 0, A046523(A156552(n)));
v350064 = rgs_transform(vector(up_to, n, A350062(n)));
A350064(n) = v350064[n];
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 29 2022
STATUS
approved