A336474 - OEIS

A336474

Lexicographically earliest infinite sequence such that a(i) = a(j) => A278221(i) = A278221(j) and A329697(i) = A329697(j), for all i, j >= 1.

1, 2, 3, 2, 4, 5, 6, 2, 7, 8, 9, 5, 10, 11, 12, 2, 13, 14, 15, 8, 16, 17, 18, 5, 19, 20, 21, 11, 22, 23, 24, 2, 25, 26, 27, 14, 28, 29, 30, 8, 31, 32, 33, 17, 34, 35, 36, 5, 37, 12, 38, 20, 39, 40, 25, 11, 41, 42, 43, 23, 44, 45, 46, 2, 47, 48, 49, 26, 50, 32, 51, 14, 52, 53, 34, 29, 54, 55, 56, 8, 57, 58, 59, 32, 60, 61, 62, 17, 63, 64, 65, 35, 66, 67, 68, 5, 69, 70, 71, 12, 72, 73, 74, 20, 75

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OFFSET

1,2

COMMENTS

Restricted growth sequence transform of the ordered pair [A278221(n), A329697(n)].

For all i, j: A324400(i) = A324400(j) => A336146(i) = A336146(j) => a(i) = a(j).

LINKS

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

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; };

A122111(n) = if(1==n, n, my(f=factor(n), es=Vecrev(f[, 2]), is=concat(apply(primepi, Vecrev(f[, 1])), [0]), pri=0, m=1); for(i=1, #es, pri += es[i]; m *= prime(pri)^(is[i]-is[1+i])); (m));

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

A278221(n) = A046523(A122111(n));

A329697(n) = if(!bitand(n, n-1), 0, 1+A329697(n-(n/vecmax(factor(n)[, 1]))));

Aux336474(n) = [A278221(n), A329697(n)];

v336474 = rgs_transform(vector(up_to, n, Aux336474(n)));

A336474(n) = v336474[n];

CROSSREFS

Cf. A046523, A122111, A278221, A329697.

Cf. also A324400, A336146, A336473.

Sequence in context: A336154 A323234 A336156 * A336148 A336149 A336146

Adjacent sequences: A336471 A336472 A336473 * A336475 A336476 A336477

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jul 25 2020

STATUS

approved