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A336160
Lexicographically earliest infinite sequence such that a(i) = a(j) => A335915(i) = A335915(j) and A336158(i) = A336158(j), for all i, j >= 1.
6
1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5, 2, 6, 3, 7, 1, 8, 4, 9, 3, 7, 5, 10, 2, 11, 6, 12, 3, 13, 7, 5, 1, 14, 8, 15, 4, 16, 9, 17, 3, 13, 7, 18, 5, 19, 10, 20, 2, 11, 11, 15, 6, 21, 12, 22, 3, 22, 13, 23, 7, 24, 5, 19, 1, 25, 14, 26, 8, 27, 15, 28, 4, 29, 16, 30, 9, 22, 17, 31, 3, 32, 13, 33, 7, 34, 18, 35, 5, 36, 19, 25, 10, 14, 20, 37, 2, 38, 11, 39, 11, 40, 15, 41, 6, 42
OFFSET
1,3
COMMENTS
Restricted growth sequence transform of the ordered pair [A335915(n), A336158(n)].
For all i, j: A324400(i) = A324400(j) => a(i) = a(j) => A336161(i) = A336161(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; };
A000265(n) = (n>>valuation(n, 2));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
A335915(n) = { my(f=factor(n)); prod(k=1, #f~, if(2==f[k, 1], 1, (A000265(f[k, 1]-1)*A000265(f[k, 1]+1))^f[k, 2])); };
Aux336160(n) = [A335915(n), A336158(n)];
v336160 = rgs_transform(vector(up_to, n, Aux336160(n)));
A336160(n) = v336160[n];
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jul 11 2020
STATUS
approved