A328397 - OEIS

A328397

Lexicographically earliest infinite sequence such that a(i) = a(j) => A328400(A276087(i)) = A328400(A276087(j)) for all i, j.

1, 1, 1, 1, 1, 2, 3, 3, 3, 1, 3, 2, 4, 5, 3, 6, 3, 3, 7, 3, 8, 9, 8, 10, 11, 12, 13, 14, 15, 16, 1, 3, 5, 3, 3, 4, 3, 3, 17, 1, 17, 2, 18, 19, 17, 6, 20, 4, 7, 21, 17, 22, 23, 24, 25, 26, 27, 28, 23, 21, 5, 5, 4, 7, 17, 7, 3, 3, 17, 29, 30, 31, 18, 19, 32, 22, 33, 24, 34, 35, 36, 37, 38, 39, 15, 40, 41, 14, 42, 43, 7, 19, 44, 45, 19, 46, 21, 8, 17, 47, 48, 4, 49

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,6

COMMENTS

Restricted growth sequence transform of function f(n) = A328400(A276087(n)).

For all i, j:

A328395(i) = A328395(j) => a(i) = a(j) => A328389(i) = A328389(j).

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..32589

Index entries for sequences related to primorial base

PROG

(PARI)

up_to = 32589;

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; };

A007947(n) = factorback(factorint(n)[, 1]);

A181819(n) = factorback(apply(e->prime(e), (factor(n)[, 2])));

A181821(n) = { my(f=factor(n), p=0, m=1); forstep(i=#f~, 1, -1, while(f[i, 2], f[i, 2]--; m *= (p=nextprime(p+1))^primepi(f[i, 1]))); (m); };

A328400(n) = A181821(A007947(A181819(n)));

A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };

A276087(n) = A276086(A276086(n));

v328397 = rgs_transform(vector(1+up_to, n, A328400(A276087(n-1))));

A328397(n) = v328397[1+n];

CROSSREFS

Cf. A276086, A276087, A328389, A328400.

Cf. also A278226, A286626, A328388, A328395, A328396.

Sequence in context: A171576 A016738 A061911 * A082239 A207814 A062745

Adjacent sequences: A328394 A328395 A328396 * A328398 A328399 A328400

KEYWORD

nonn

AUTHOR

Antti Karttunen, Oct 15 2019

STATUS

approved