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

1,15

Comments

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

Links

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

Formula

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A008472, A183063.

Sequence in context: A180017 A243827 A059530 * A049828 A342557 A286131

Adjacent sequences: A193522 A193523 A193524 * A193526 A193527 A193528

Keyword

nonn

Author

Michel Lagneau, Jul 29 2011

Status

approved