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%I #19 Jan 27 2024 17:44:14
%S 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,
%T 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,
%U 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
%N a(n) = tau(n) + omega(n).
%C Here tau(n) is the number of divisors of n (A000005) and omega(n) is the number distinct primes dividing n (A001221).
%H G. C. Greubel, <a href="/A163523/b163523.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A000005(n) + A001221(n).
%F a(n) = Sum_{d|n} (1 + c(d)), where c = A010051. - _Wesley Ivan Hurt_, Jan 27 2024
%p 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
%t Array[DivisorSigma[0,#]+PrimeNu[#]&,100] (* _Harvey P. Dale_, Dec 03 2011 *)
%o (PARI) for(n=1,50, print1(numdiv(n) + omega(n), ", ")) \\ _G. C. Greubel_, May 16 2017
%o (Magma) [#PrimeDivisors(n)+NumberOfDivisors(n): n in [1..100]]; // _Vincenzo Librandi_, May 17 2017
%Y Cf. A000005, A000027, A001221, A010051.
%K nonn,easy
%O 1,2
%A _Juri-Stepan Gerasimov_, Jul 30 2009
%E a(40) and a(49) corrected by _R. J. Mathar_, Aug 01 2009
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