A351441 Lexicographically earliest infinite sequence such that a(i) = a(j) => A003557(i) = A003557(j) and A351450(i) = A351450(j) for all i, j >= 1.

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

Offset: 1

Author

Antti Karttunen, Feb 12 2022

Keywords

• nonn

Comments

Restricted growth sequence transform of the ordered pair [A003557(n), A351450(n)].

For all i, j >= 1:

a(i) = a(j) => A326042(i) = A326042(j),

a(i) = a(j) => A351455(i) = A351455(j).

Links

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

Crossrefs

Cf. A003557, A003961, A048250, A064989, A326042, A351450, A351455.

Cf. also A291751, A351461.

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; };
A003557(n) = (n/factorback(factorint(n)[, 1]));
A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A048250(n) = factorback(apply(p -> p+1,factor(n)[,1]));
A064989(n) = { my(f = factor(n>>valuation(n,2))); for(i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f); };
A351450(n) = A064989(A048250(A003961(n)));
Aux351441(n) = [A003557(n), A351450(n)];
v351441 = rgs_transform(vector(up_to, n, Aux351441(n)));
A351441(n) = v351441[n];