A163523 a(n) = tau(n) + omega(n).

1, 3, 3, 4, 3, 6, 3, 5, 4, 6, 3, 8, 3, 6, 6, 6, 3, 8, 3, 8, 6, 6, 3, 10, 4, 6, 5, 8, 3, 11, 3, 7, 6, 6, 6, 11, 3, 6, 6, 10, 3, 11, 3, 8, 8, 6, 3, 12, 4, 8, 6, 8, 3, 10, 6, 10, 6, 6, 3, 15, 3, 6, 8, 8, 6, 11, 3, 8, 6, 11, 3, 14, 3, 6, 8, 8, 6, 11, 3, 12, 6, 6, 3, 15, 6, 6, 6, 10, 3, 15, 6, 8, 6, 6, 6, 14

Offset: 1

Author

Juri-Stepan Gerasimov, Jul 30 2009

Keywords

• nonn
• easy

Comments

Here tau(n) is the number of divisors of n (A000005) and omega(n) is the number distinct primes dividing n (A001221).

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A000027, A001221, A010051.

Programs

Magma

[#PrimeDivisors(n)+NumberOfDivisors(n): n in [1..100]]; // Vincenzo Librandi, May 17 2017

Maple

A001221 := proc(n) nops(numtheory[factorset](n)) ; end: A163523 := proc(n) numtheory[tau](n)+A001221(n) ; end: seq(A163523(n),n=1..120) ; # R. J. Mathar, Aug 01 2009

Mathematica

Array[DivisorSigma[0,#]+PrimeNu[#]&,100] (* Harvey P. Dale, Dec 03 2011 *)

PARI

for(n=1,50, print1(numdiv(n) + omega(n), ", ")) \\ G. C. Greubel, May 16 2017

Formula

a(n) = A000005(n) + A001221(n).

a(n) = Sum_{d|n} (1 + c(d)), where c = A010051. - Wesley Ivan Hurt, Jan 27 2024

Extensions

a(40) and a(49) corrected by R. J. Mathar, Aug 01 2009