A344594 Lexicographically earliest infinite sequence such that a(i) = a(j) => A342920(i) = A342920(j), for all i, j >= 1.

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

Offset: 1

Author

Antti Karttunen, May 26 2021

Keywords

• nonn

Comments

Restricted growth sequence transform of A342920, where A342920(n) = A342002(A108951(n)) = A329047(n) / A344592(n).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences related to primorial base
• Index entries for sequences related to primorial numbers

Crossrefs

Cf. A108951, A324886, A329047, A342002, A342920, A344592.

Cf. also A344593.

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; };
A034386(n) = prod(i=1, primepi(n), prime(i));
A108951(n) = { my(f=factor(n)); prod(i=1, #f~, A034386(f[i, 1])^f[i, 2]) };  \\ From A108951
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A003557(n) = (n/factorback(factorint(n)[, 1]));
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A342002(n) = { my(u=A276086(n)); (A003415(u) / A003557(u)); };
A342920(n) = A342002(A108951(n));
v344594 = rgs_transform(vector(up_to, n, A342920(n)));
A344594(n) = v344594[n];