A319989 a(n) = A303757(A252463(n)).

1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 3, 1, 1, 3, 2, 1, 2, 1, 3, 3, 1, 1, 4, 2, 1, 2, 3, 1, 1, 1, 2, 3, 1, 1, 4, 1, 1, 2, 3, 1, 2, 1, 2, 4, 1, 1, 4, 1, 1, 3, 3, 1, 2, 2, 4, 3, 1, 1, 5, 1, 1, 3, 2, 2, 2, 1, 3, 3, 1, 1, 5, 1, 1, 4, 3, 1, 2, 1, 4, 2, 1, 1, 6, 2, 1, 2, 3, 1, 3, 2, 2, 2, 1, 1, 5, 1, 2, 4, 4, 1, 1, 1, 4, 5

Offset

1,8

Links

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

Formula

a(n) = A303757(A252463(n)).

Mathematica

Block[{s = Table[Which[n == 1, 1, EvenQ@n, n/2, True, Times @@ Power[Which[# == 1, 1, # == 2, 1, True, NextPrime[#, -1]] & /@ First@ #, Last@ #] &@ Transpose@ FactorInteger@ n], {n, 120}], t}, t = EulerPhi@ Range@ Max@ s; Map[Function[n, Count[t[[2 ;; n]], _?(# == t[[n]] &)]], s] /. 0 -> 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];
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1, 1]==2), f[1, 2] = 0); for (i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f)};
A252463(n) = if(!(n%2), n/2, A064989(n));
A319989(n) = A303757(A252463(n));

Crossrefs

Cf. A252463, A303757.

Cf. also A319699, A319700, A319703, A320107, A320111.

Sequence in context: A326644 A120964 A318810 * A338117 A353468 A184305

Adjacent sequences: A319986 A319987 A319988 * A319990 A319991 A319992

Keyword

nonn

Author

Antti Karttunen, Nov 22 2018

Status

approved