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A368695
Lexicographically earliest infinite sequence such that a(i) = a(j) => A368694(i) = A368694(j) for all i, j >= 0.
2
1, 2, 3, 4, 3, 5, 6, 7, 3, 8, 9, 10, 3, 11, 12, 13, 3, 14, 15, 13, 3, 16, 17, 18, 3, 19, 13, 20, 3, 21, 11, 4, 3, 22, 23, 24, 3, 21, 11, 25, 3, 26, 27, 28, 3, 29, 30, 5, 3, 31, 32, 33, 3, 8, 34, 21, 3, 35, 36, 11, 3, 20, 6, 7, 3, 37, 38, 39, 3, 40, 41, 42, 3, 35, 36, 43, 3, 44, 45, 8, 3, 46, 47, 48, 3, 49, 50, 35, 3
OFFSET
0,2
COMMENTS
Restricted growth sequence transform of A368694, where A368694 is the Dirichlet inverse of the highest power of two that divides sigma(n), applied to A163511(n).
LINKS
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; };
A082903(n) = (2^valuation(sigma(n), 2));
memoA366889 = Map();
A366889(n) = if(1==n, 1, my(v); if(mapisdefined(memoA366889, n, &v), v, v = -sumdiv(n, d, if(d<n, A082903(n/d)*A366889(d), 0)); mapput(memoA366889, n, v); (v)));
A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
v368695 = rgs_transform(vector(1+up_to, n, A368694(n-1)));
A368695(n) = v368695[1+n];
CROSSREFS
KEYWORD
nonn,look
AUTHOR
Antti Karttunen, Jan 03 2024
STATUS
approved