A328471 - OEIS

A328471

Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(A328461(i)) = A046523(A328461(j)) for all i, j.

1, 1, 2, 1, 2, 3, 3, 1, 2, 4, 5, 5, 2, 2, 5, 1, 2, 5, 5, 6, 5, 2, 5, 7, 2, 3, 8, 2, 5, 9, 5, 1, 2, 6, 9, 5, 5, 5, 5, 10, 2, 2, 10, 5, 2, 5, 11, 9, 2, 5, 9, 2, 9, 11, 9, 5, 2, 12, 10, 10, 2, 2, 5, 1, 5, 13, 12, 5, 9, 5, 14, 10, 5, 2, 10, 2, 5, 5, 12, 15, 2, 2, 10, 3, 10, 12, 9, 2, 2, 16, 5, 12, 10, 2, 5, 5, 2, 5, 5, 9, 5, 5, 10, 5, 2

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OFFSET

1,3

COMMENTS

Restricted growth sequence transform of function f(n) = A046523(A276156(n)/A002110(A007814(n))).

LINKS

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

Index entries for sequences related to binary expansion of n

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; };

A002110(n) = prod(i=1, n, prime(i));

A276156(n) = { my(p=2, pr=1, s=0); while(n, if(n%2, s += pr); n >>= 1; pr *= p; p = nextprime(1+p)); (s); };

A328461(n) = (A276156(n)/A002110(valuation(n, 2)));

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

v328471 = rgs_transform(vector(up_to, n, A046523(A328461(n))));

A328471(n) = v328471[n];

CROSSREFS

Cf. A002110, A007814, A046523, A276156, A328461, A328472, A328474.

Sequence in context: A100002 A376238 A348330 * A227909 A301984 A210805

Adjacent sequences: A328468 A328469 A328470 * A328472 A328473 A328474

KEYWORD

nonn

AUTHOR

Antti Karttunen, Oct 18 2019

STATUS

approved