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
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
KEYWORD
nonn
AUTHOR
Michel Lagneau, Jul 29 2011
STATUS
approved