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%I A103445 #7 Jul 22 2024 15:24:21
%S A103445 1,2,4,6,10,14,22,22,30,46,74,94,90,102,130,170,198,222,290,350,474,
%T A103445 650,730,734,746,838,962,1214,2138,2582,1890,1830,2526,3498,4746,6842,
%U A103445 5098,6358,8178,10634,8650,9782,13634,14438,17178,20202,22170,21422,16298
%N A103445 Sum of the numbers of unitary divisors of the binomial coefficients C(n,k), k=0..n.
%C A103445 Row sums of the triangle A103444.
%e A103445 a(3) = 6 because the divisors of 1,3,3,1 are {1},{1,3},{1,3},{1}, respectively, all of which are unitary, and 1 + 2 + 2 + 1 = 6.
%p A103445 with(numtheory):unitdiv:=proc(n) local A, k: A:={}: for k from 1 to tau(n) do if gcd(divisors(n)[k],n/divisors(n)[k])=1 then A:=A union {divisors(n)[k]} else A:=A fi od end: T:=proc(n,k) if k<=n then nops(unitdiv(binomial(n,k))) else 0 fi end: for n from 0 to 50 do b[n]:=[seq(T(n,k),k=0..n)] od: seq(sum(b[n][j],j=1..n+1),n=0..50);
%t A103445 a[n_] := Sum[2^PrimeNu[Binomial[n, k]], {k, 0, n}]; Array[a, 50, 0] (* _Amiram Eldar_, Jul 22 2024 *)
%o A103445 (PARI) a(n) = sum(k = 0, n, 2^omega(binomial(n, k))); \\ _Amiram Eldar_, Jul 22 2024
%Y A103445 Cf. A007318, A034444, A103444.
%K A103445 nonn
%O A103445 0,2
%A A103445 _Emeric Deutsch_, Feb 06 2005

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