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A163523 a(n) = tau(n) + omega(n). 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Here tau(n) is the number of divisors of n (A000005) and omega(n) is the number distinct primes dividing n (A001221).
LINKS
FORMULA
a(n) = A000005(n) + A001221(n).
a(n) = Sum_{d|n} (1 + c(d)), where c = A010051. - Wesley Ivan Hurt, Jan 27 2024
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 *)
PROG
(PARI) for(n=1, 50, print1(numdiv(n) + omega(n), ", ")) \\ G. C. Greubel, May 16 2017
(Magma) [#PrimeDivisors(n)+NumberOfDivisors(n): n in [1..100]]; // Vincenzo Librandi, May 17 2017
CROSSREFS
Sequence in context: A130896 A254279 A029882 * A151664 A083503 A342137
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
a(40) and a(49) corrected by R. J. Mathar, Aug 01 2009
STATUS
approved

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Last modified April 23 11:22 EDT 2024. Contains 371913 sequences. (Running on oeis4.)