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Sum of even divisors of sopf(n).
1

%I #14 Oct 22 2024 02:53:25

%S 0,2,0,2,0,0,0,2,0,0,0,0,0,0,14,2,0,0,0,0,12,0,0,0,0,0,0,0,0,12,0,2,

%T 16,0,24,0,0,0,30,0,0,24,0,0,14,0,0,0,0,0,36,0,0,0,30,0,24,0,0,12,0,0,

%U 12,2,26,30,0,0,28,16,0,0,0,0,14,0,26,26,0,0

%N Sum of even divisors of sopf(n).

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

%H Antti Karttunen, <a href="/A193526/b193526.txt">Table of n, a(n) for n = 1..20000</a>

%F a(1) = 0; for n > 1, a(n) = A146076(A008472(n)). - _Antti Karttunen_, Dec 23 2018

%t Table[Total[Select[Divisors[Plus @@ First[Transpose[FactorInteger[n]]]], EvenQ[#] &]], {n, 100}]

%o (PARI)

%o A008472(n) = vecsum(factor(n)[, 1]); \\ From A008472

%o A146076(n) = if (n%2, 0, 2*sigma(n/2)); \\ From A146076

%o A193526(n) = if(1==n,0,A146076(A008472(n))); \\ _Antti Karttunen_, Dec 23 2018

%Y Cf. A008472, A146076, A193525.

%K nonn,easy

%O 1,2

%A _Michel Lagneau_, Jul 29 2011