A355830 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(i) = A046523(j) and A345000(i) = A345000(j) for all i, j >= 1.

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

Offset

1,2

Comments

Restricted growth sequence transform of the ordered pair [A046523(n), A345000(n)].

For all i, j: A351235(i) = A351235(j) => a(i) = a(j).

Links

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

Index entries for sequences related to primorial base

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; };
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A345000(n) = gcd(A003415(n), A003415(A276086(n)));
Aux355830(n) = [A046523(n), A345000(n)];
v355830 = rgs_transform(vector(up_to, n, Aux355830(n)));
A355830(n) = v355830[n];

Crossrefs

Cf. A003415, A046523, A276086, A345000.

Cf. also A351235, A355000, A355831, A355832, A355836.

Sequence in context: A218701 A305790 A294877 * A355831 A300223 A351949

Adjacent sequences: A355827 A355828 A355829 * A355831 A355832 A355833

Keyword

nonn

Author

Antti Karttunen, Jul 20 2022

Status

approved