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A366800
Lexicographically earliest infinite sequence such that a(i) = a(j) => A366799(i) = A366799(j) for all i, j >= 0, where A366799 is the number of divisors d of n that are not of the form 4k+2, as permuted by the Doudna sequence.
2
1, 1, 2, 2, 2, 2, 3, 3, 2, 2, 4, 4, 3, 3, 4, 4, 2, 2, 4, 4, 4, 4, 5, 5, 3, 3, 5, 5, 4, 4, 6, 6, 2, 2, 4, 4, 4, 4, 5, 5, 4, 4, 7, 7, 5, 5, 7, 7, 3, 3, 5, 5, 5, 5, 8, 8, 4, 4, 7, 7, 6, 6, 5, 5, 2, 2, 4, 4, 4, 4, 5, 5, 4, 4, 7, 7, 5, 5, 7, 7, 4, 4, 7, 7, 7, 7, 9, 9, 5, 5, 9, 9, 7, 7, 10, 10, 3, 3, 5, 5, 5, 5, 8, 8
OFFSET
0,3
COMMENTS
Restricted growth sequence transform of A366799.
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; };
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
A320111(n) = sumdiv(n, d, (2!=(d%4)));
A366799(n) = A320111(A005940(1+n));
v366800 = rgs_transform(vector(1+up_to, n, A366799(n-1)));
A366800(n) = v366800[1+n];
CROSSREFS
Cf. also A366798.
Sequence in context: A081743 A247069 A367008 * A366799 A322168 A118377
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 27 2023
STATUS
approved