A247087 a(n) = pi(phi(p(P(n)))) = A000720(A000010(A000041(A000040(n)))).

0, 1, 3, 4, 9, 25, 41, 39, 168, 462, 442, 1939, 2571, 3998, 5123, 17040, 24853, 38887, 195022, 183430, 404386, 381060, 1162366, 2105509, 1799881, 5966593, 5380661, 14184985, 10473967, 22631261, 135452589, 109540327, 244730051, 487610708, 604467085, 671043205, 3350187738

Offset: 1

Author

Alois P. Heinz, Mar 14 2015

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..90 (calculated using Kim Walisch's primecount)
• Kim Walisch, Fast C++ prime counting function implementation (primecount).

Crossrefs

Cf. A000010, A000040, A000041, A000720, A058697, A058698, A070804.

Programs

Maple

with(numtheory): with(combinat): p:=numbpart: P:=ithprime:
a:= n-> pi(phi(p(P(n)))):
seq(a(n), n=1..20);

Mathematica

a[n_] := PrimePi @ EulerPhi @ PartitionsP @ Prime @ n;
Table[a[n], {n, 1, 30}] (* Jean-François Alcover, Mar 25 2017 *)

Formula

a(n) = A070804(A058698(n)) = A000720(A000010(A000041(A000040(n)))).

Extensions

a(31)-a(37) from Amiram Eldar, Sep 03 2024