A193525 Number of even divisors of sopf(n).

0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 3, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 2, 0, 4, 0, 0, 0, 4, 0, 0, 4, 0, 0, 3, 0, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 2, 0, 0, 2, 0, 0, 2, 1, 3, 4, 0, 0, 2, 2, 0, 0, 0, 0, 3, 0, 3, 3, 0, 0, 0, 0, 0, 4, 2, 0

Offset: 1

Author

Michel Lagneau, Jul 29 2011

Keywords

• nonn

Comments

Sopf(n) is the sum of the distinct primes dividing n (A008472).

Examples

			a(15) = 3 because sopf(15) = 8 and its 3 even divisors are {2, 4, 8}.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A008472, A183063.

Programs

Mathematica

f[n_] := Block[{d=Divisors[Plus@@First[Transpose[FactorInteger[n]]]]}, Count[EvenQ[d],True]]; Table[f[n] ,{n,100}]
Array[Count[Divisors[Total[FactorInteger[#][[All,1]]]],?EvenQ]&,100] (* _Harvey P. Dale, Jun 20 2019 *)
even[n_] := (e = IntegerExponent[n, 2]) * DivisorSigma[0, n / 2^e];  a[n_] := even[Plus @@ FactorInteger[n][[;;, 1]]]; Array[a, 100] (* Amiram Eldar, Jul 06 2022 *)

PARI

sopf(n:int)=my(f=factor(n)[,1]); sum(i=1,#f,f[i])
a(n)=if(n==1,0,n=sopf(n);if(n%2,0,numdiv(n/2))) \\ Charles R Greathouse IV, Jul 31 2011

Formula

a(n) = A183063(A008472(n)). - Amiram Eldar, Jul 06 2022