A093320 a(1) = 1; for m >= 2, a(m) = sum{p|m} a(pi(p)), where the sum is over the distinct prime divisors p of m and pi(p) is the order of p among the primes = the number of primes <= p.

1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 2, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 2, 1, 3, 1, 2, 2, 3, 1, 1, 2, 2, 2, 2, 2, 2, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 1, 2, 2, 3, 1, 2, 2, 2, 2, 3, 1, 3, 2, 2, 2, 1, 3, 3, 1, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 4, 2, 2, 1, 3, 1, 3, 2, 3, 3, 2, 2, 3, 3, 2, 2, 3, 2, 2, 1, 2, 2, 2, 3, 3, 1, 3, 3

Offset: 1

Author

Leroy Quet, Apr 26 2004

Keywords

• nonn
• easy

Crossrefs

Cf. A093321, A066328, A094162 (for where n first appears).

Programs

Mathematica

PrimeFactors[n_Integer] := Flatten[ Table[ # [[1]], {1}] & /@ FactorInteger[n]]; a[1] = 1; a[n_] := a[n] = (Plus @@ (a[ # ] & /@ PrimePi[ PrimeFactors[n]])); Table[ a[n], {n, 105}] (* Robert G. Wilson v, May 04 2004 *)

Extensions

More terms from Robert G. Wilson v, May 04 2004