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

1,3

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?

Links

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

Example

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

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

Crossrefs

Cf. A000593.

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

Sequence in context: A336933 A336460 A108712 * A351461 A336936 A366886

Adjacent sequences: A351034 A351035 A351036 * A351038 A351039 A351040

Keyword

nonn,easy,look

Author

Antti Karttunen, Jan 31 2022

Status

approved