A344772 Ordinal transform of infinitary phi, A091732.

1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 3, 2, 1, 1, 3, 1, 2, 3, 2, 1, 4, 1, 4, 2, 2, 1, 4, 1, 2, 1, 3, 2, 3, 1, 3, 4, 5, 1, 6, 1, 2, 1, 2, 1, 3, 1, 5, 2, 2, 1, 4, 2, 4, 3, 2, 1, 6, 1, 4, 2, 1, 3, 2, 1, 4, 1, 7, 1, 8, 1, 4, 5, 1, 2, 9, 1, 3, 1, 3, 1, 5, 1, 2, 1, 5, 1, 3, 2, 2, 4, 2, 3, 6, 1, 6, 2, 4, 1, 4, 1, 6, 7

Offset

1,2

Comments

Number of values of k, 1 <= k <= n, with A091732(k) = A091732(n).

Links

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

Mathematica

f[p_, e_] := p^(2^(-1 + Position[Reverse @ IntegerDigits[e, 2], 1]));
iphi[1] = 1; iphi[n_] := Times @@ (Flatten@(f @@@ FactorInteger[n]) - 1);
b[_] = 0;
a[n_] := a[n] = With[{t = iphi[n]}, b[t] = b[t] + 1];
Array[a, 105] (* Jean-François Alcover, Dec 27 2021, after Amiram Eldar in A091732 *)

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; };
ispow2(n) = (n && !bitand(n, n-1));
A302777(n) = ispow2(isprimepower(n));
A091732(n) = { my(m=1); while(n > 1, fordiv(n, d, if((d<n)&&A302777(n/d), m *= ((n/d)-1); n = d; break))); (m); };
v344772 = ordinal_transform(vector(up_to, n, A091732(n)));
A344772(n) = v344772[n];

Crossrefs

Cf. A091732, A050376, A302777.

Cf. also A081373 (ordinal transform of phi), A303756 (of Carmichael's lambda), A330739 (of unitary phi).

Sequence in context: A330665 A345985 A103765 * A307610 A125029 A339839

Adjacent sequences: A344769 A344770 A344771 * A344773 A344774 A344775

Keyword

nonn,look

Author

Antti Karttunen, May 31 2021

Status

approved