A332826 - OEIS

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A332826

Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(A332824(i)) = A046523(A332824(j)) for all i, j.

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

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; };

A019565(n) = {my(j, v); factorback(Mat(vector(if(n, #n=vecextract(binary(n), "-1..1")), j, [prime(j), n[j]])~))}; \\ From A019565

A332824(n) = { my(m=1); fordiv(n, d, m *= A019565(eulerphi(d))); (m); };

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

v332826 = rgs_transform(vector(up_to, n, A046523(A332824(n))));

A332826(n) = v332826[n];

CROSSREFS

Cf. A000010, A019565, A046523, A332824, A332827.

Cf. A019434 (positions of 3's).

Cf. also A318835.

Sequence in context: A160180 A319351 A323373 * A353840 A319350 A336855

Adjacent sequences: A332823 A332824 A332825 * A332827 A332828 A332829

KEYWORD

nonn

AUTHOR

Antti Karttunen, Feb 25 2020

STATUS

approved