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A336392
Lexicographically earliest infinite sequence such that a(i) = a(j) => A278222(i) = A278222(j) and A336467(i) = A336467(j), for all i, j >= 1.
3
1, 1, 2, 1, 3, 2, 4, 1, 5, 3, 6, 2, 7, 4, 8, 1, 9, 5, 10, 3, 11, 6, 12, 2, 13, 7, 14, 4, 15, 8, 16, 1, 3, 9, 6, 5, 17, 10, 18, 3, 19, 11, 20, 6, 21, 12, 22, 2, 23, 13, 24, 7, 25, 14, 26, 4, 27, 15, 28, 8, 29, 16, 30, 1, 31, 3, 32, 9, 33, 6, 34, 5, 35, 17, 36, 10, 21, 18, 37, 3, 11, 19, 38, 11, 39, 20, 40, 6, 41, 21, 42, 12, 43, 22, 44, 2, 45, 23, 46, 13
OFFSET
1,3
COMMENTS
Restricted growth sequence transform of the ordered pair [A278222(n), A336467(n)].
For all i, j: A324400(i) = A324400(j) => A003602(i) = A003602(j) => a(i) = a(j).
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; };
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
A278222(n) = A046523(A005940(1+n));
A000265(n) = (n>>valuation(n, 2));
A336467(n) = { my(f=factor(n)); prod(k=1, #f~, if(2==f[k, 1], 1, (A000265(f[k, 1]+1))^f[k, 2])); };
Aux336392(n) = [A278222(n), A336467(n)];
v336392 = rgs_transform(vector(up_to, n, Aux336392(n)));
A336392(n) = v336392[n];
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Aug 10 2020
STATUS
approved