A366294 Lexicographically earliest infinite sequence such that a(i) = a(j) => A326042(i) = A326042(j) for all i, j >= 1, where A326042(n) = A064989(sigma(A003961(n))).

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

Offset: 1

Author

Antti Karttunen, Oct 07 2023

Keywords

• nonn

Comments

Restricted growth sequence transform of A326042.

Links

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

Crossrefs

Cf. A000203, A003961, A064989, A326042.

Cf. also A286603, A366295.

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; };
A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A064989(n) = { my(f=factor(n>>valuation(n,2))); for(i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f); };
A326042(n) = A064989(sigma(A003961(n)));
v366294  = rgs_transform(vector(up_to,n,A326042(n)));
A366294(n) = v366294[n];