A336472 - OEIS

A336472

Lexicographically earliest infinite sequence such that a(i) = a(j) => A278222(i) = A278222(j) and A336466(i) = A336466(j), for all i, j >= 1.

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

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OFFSET

1,3

COMMENTS

Restricted growth sequence transform of the ordered pair [A278222(n), A336466(n)].

For all i, j: A336460(i) = A336460(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; };

A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };

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

A278222(n) = A046523(A005940(1+n));

A000265(n) = (n>>valuation(n, 2));

A336466(n) = { my(f=factor(n)); prod(k=1, #f~, if(2==f[k, 1], 1, (A000265(f[k, 1]-1))^f[k, 2])); };

Aux336472(n) = [A278222(n), A336466(n)];

v336472 = rgs_transform(vector(up_to, n, Aux336472(n)));

A336472(n) = v336472[n];

CROSSREFS

Cf. A278222, A336466.

Cf. also A336162, A336460, A336470, A336471, A336473.

Sequence in context: A124172 A349191 A336394 * A058933 A087470 A373215

Adjacent sequences: A336469 A336470 A336471 * A336473 A336474 A336475

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jul 24 2020

STATUS

approved