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A303757 a(1) = 1 and for n > 1, a(n) = number of values of k, 2 <= k <= n, with A000010(k) = A000010(n), where A000010 is Euler totient function phi. 6
1, 1, 1, 2, 1, 3, 1, 2, 2, 3, 1, 4, 1, 3, 1, 2, 1, 4, 1, 3, 2, 2, 1, 4, 1, 3, 2, 4, 1, 5, 1, 2, 2, 3, 1, 5, 1, 3, 2, 4, 1, 6, 1, 3, 3, 2, 1, 5, 2, 4, 1, 4, 1, 4, 2, 5, 2, 2, 1, 6, 1, 2, 3, 2, 1, 5, 1, 3, 1, 6, 1, 7, 1, 4, 3, 5, 2, 8, 1, 4, 1, 4, 1, 9, 1, 3, 1, 5, 1, 10, 2, 2, 3, 2, 3, 5, 1, 4, 4, 6, 1, 6, 1, 2, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Ordinal transform of f, where f(1) = 0 and f(n) = A000010(n) for n > 1.

After a(1)=1 and a(4)=2, the positions of the rest of records is given by A081375(n) = 6, 12, 30, 42, 72, 78, 84, 90, 190, ..., for n >= 3.

Apart from a(2) = 1, the other positions of 1's is given by A210719.

LINKS

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

FORMULA

Except for a(2) = 1, a(n) = A081373(n).

MATHEMATICA

With[{s = EulerPhi@ Range@ 105}, MapAt[# + 1 &, Table[Count[s[[2 ;; n]], _?(# == s[[n]] &)], {n, Length@ s}], 1]] (* Michael De Vlieger, Nov 23 2018 *)

PROG

(PARI)

up_to = 65537;

ordinal_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), pt); for(i=1, length(invec), if(mapisdefined(om, invec[i]), pt = mapget(om, invec[i]), pt = 0); outvec[i] = (1+pt); mapput(om, invec[i], (1+pt))); outvec; };

Aux303757(n) = if(1==n, 0, eulerphi(n));

v303757 = ordinal_transform(vector(up_to, n, Aux303757(n)));

A303757(n) = v303757[n];

CROSSREFS

Cf. A000010, A081373, A081375, A210719, A303754, A303758, A303777.

Sequence in context: A293435 A294901 A305818 * A323014 A182850 A293227

Adjacent sequences:  A303754 A303755 A303756 * A303758 A303759 A303760

KEYWORD

nonn

AUTHOR

Antti Karttunen, Apr 30 2018

STATUS

approved

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Last modified January 20 14:26 EST 2020. Contains 331094 sequences. (Running on oeis4.)