A332827 - OEIS

A332827

Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = A003557(A332824(n)) for all other numbers, except f(1) = 0.

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

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OFFSET

1,2

COMMENTS

For all i, j:

A305801(i) = A305801(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; };

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); };

A003557(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 2] = f[i, 2]-1); factorback(f); };

Aux332827(n) = if(1==n, 0, A003557(A332824(n)));

v332827 = rgs_transform(vector(up_to, n, Aux332827(n)));

A332827(n) = v332827[n];

CROSSREFS

Cf. A000010, A003557, A019565, A305801, A332824, A332826.

Cf. also A324538.

Sequence in context: A323235 A086374 A322591 * A325811 A324380 A123182

Adjacent sequences: A332824 A332825 A332826 * A332828 A332829 A332830

KEYWORD

nonn

AUTHOR

Antti Karttunen, Feb 25 2020

STATUS

approved