A336161 Lexicographically earliest infinite sequence such that a(i) = a(j) => A087436(i) = A087436(j) and A335915(i) = A335915(j) for all i, j >= 1.

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, 11, 4, 15, 9, 16, 3, 13, 7, 17, 5, 18, 10, 19, 2, 11, 11, 11, 6, 20, 12, 21, 3, 21, 13, 22, 7, 23, 5, 18, 1, 24, 14, 25, 8, 26, 11, 27, 4, 28, 15, 29, 9, 21, 16, 30, 3, 31, 13, 32, 7, 33, 17, 34, 5, 35, 18, 24, 10, 14, 19, 36, 2, 37, 11, 38, 11, 39, 11, 40, 6, 29

Offset: 1

Author

Antti Karttunen, Jul 10 2020

Keywords

• nonn

Comments

Restricted growth sequence transform of the ordered pair [A087436(n), A335915(n)].

For all i, j: A324400(i) = A324400(j) => a(i) = a(j) => A335904(i) = A335904(j).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A087436, A335915.

Cf. also A324400, A335880, A335904.

Programs

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; };
A087436(n) = (bigomega(n>>valuation(n,2)));
A000265(n) = (n>>valuation(n,2));
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])); };
Aux336161(n) = [A087436(n),A335915(n)];
v336161 = rgs_transform(vector(up_to, n, Aux336161(n)));
A336161(n) = v336161[n];