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A328470 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(i) = A046523(j) and A053669(i) = A053669(j) for all i, j. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A318888 A323079 A331174 * A322810 A322024 A326203

Adjacent sequences:  A328467 A328468 A328469 * A328471 A328472 A328473

KEYWORD

nonn

AUTHOR

Antti Karttunen, Oct 19 2019

STATUS

approved

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Last modified June 16 12:45 EDT 2021. Contains 345057 sequences. (Running on oeis4.)