A328469 - OEIS

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A328469

Lexicographically earliest infinite sequence such that a(i) = a(j) => A020639(i) = A020639(j) and A046523(i) = A046523(j) for all i, j.

1, 2, 3, 4, 5, 6, 7, 8, 9, 6, 10, 11, 12, 6, 13, 14, 15, 11, 16, 11, 13, 6, 17, 18, 19, 6, 20, 11, 21, 22, 23, 24, 13, 6, 25, 26, 27, 6, 13, 18, 28, 22, 29, 11, 30, 6, 31, 32, 33, 11, 13, 11, 34, 18, 25, 18, 13, 6, 35, 36, 37, 6, 30, 38, 25, 22, 39, 11, 13, 22, 40, 41, 42, 6, 30, 11, 43, 22, 44, 32, 45, 6, 46, 36, 25, 6, 13, 18, 47, 36, 43, 11, 13, 6, 25, 48, 49, 11, 30, 26, 50, 22, 51, 18, 52

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OFFSET

1,2

COMMENTS

Restricted growth sequence transform of the ordered pair [A020639(n), A046523(n)], where A020639(n) gives the smallest prime factor of n, while A046523(n) gives the prime signature of n.

For all i, 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; };

A020639(n) = if(n>1, if(n>n=factor(n, 0)[1, 1], n, factor(n)[1, 1]), 1);

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

Aux328469(n) = [A020639(n), A046523(n)];

v328469 = rgs_transform(vector(up_to, n, Aux328469(n)));

A328469(n) = v328469[n];

CROSSREFS

Cf. A020639, A046523.

Cf. also A101296, A291761, A328470, A328477, A318891, A286455.

Sequence in context: A028901 A081597 A351578 * A373229 A347105 A245351

Adjacent sequences: A328466 A328467 A328468 * A328470 A328471 A328472

KEYWORD

nonn

AUTHOR

Antti Karttunen, Oct 19 2019

STATUS

approved