A328470 - OEIS

A328470

Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(i) = A046523(j) and A053669(i) = A053669(j) for all i, j.

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

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OFFSET

1,2

COMMENTS

Restricted growth sequence transform of A286142, or equally, of the ordered pair [A046523(n), A053669(n)], where A053669(n) gives the smallest prime not dividing n, while A046523(n) gives the prime signature of n.

For all i, j:

A305801(i) = A305801(j) => a(i) = a(j) => A291761(i) = A291761(j).

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..100000

PROG

(PARI)

up_to = 100000;

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; };

A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523

A053669(n) = forprime(p=2, , if(n%p, return(p))); \\ From A053669

Aux328470(n) = [A046523(n), A053669(n)];

v328470 = rgs_transform(vector(up_to, n, Aux328470(n)));

A328470(n) = v328470[n];

CROSSREFS

Cf. A046523, A053669, A286142, A291761, A305801, A328469.

Sequence in context: A323079 A331174 A355836 * A322810 A322024 A326203

Adjacent sequences: A328467 A328468 A328469 * A328471 A328472 A328473

KEYWORD

nonn

AUTHOR

Antti Karttunen, Oct 19 2019

STATUS

approved