A351037 Lexicographically earliest infinite sequence such that a(i) = a(j) => A000593(i) = A000593(j), for all i, j >= 1, where A000593 is the sum of odd divisors function.

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

Offset: 1

Author

Antti Karttunen, Jan 31 2022

Keywords

• nonn
• easy
• look

Comments

Restricted growth sequence transform of A000593.

Question: To which set of n does the horizontal stripe at around a(n) = ~8000 correspond in the scatter plot of this sequence?

Examples

			a(21) = a(31) = 11 because A000593(21) = A000593(31) = 32, and 32 is the 11th distinct value obtained by A000593.
		

Links

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

Crossrefs

Cf. A000593.

Cf. also A286603, A347374, A351036, A351040, A351090.

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; };
v351037 = rgs_transform(vector(up_to, n, sigma(n>>valuation(n,2))));
A351037(n) = v351037[n];