A328892 - OEIS

%I #16 Oct 30 2019 20:18:08

%S 0,1,1,2,1,2,1,4,2,2,1,3,1,2,2,8,1,3,1,3,2,2,1,5,2,2,4,3,1,3,1,16,2,2,

%T 2,4,1,2,2,5,1,3,1,3,3,2,1,9,2,3,2,3,1,5,2,5,2,2,1,4,1,2,3,32,2,3,1,3,

%U 2,3,1,6,1,2,3,3,2,3,1,9,8,2,1,4,2,2,2,5,1,4

%N If n = Product (p_j^k_j) then a(n) = Sum (2^(k_j - 1)).

%H <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>

%F If n = Product (p_j^k_j) then a(n) = Sum ordered partition(k_j).

%F Additive with a(p^e) = 2^(e-1).

%e a(72) = 6 because 72 = 2^3 * 3^2 and 2^(3 - 1) + 2^(2 - 1) = 6.

%p a:= n-> add(2^(i[2]-1), i=ifactors(n)[2]):

%p seq(a(n), n=1..100);  # _Alois P. Heinz_, Oct 29 2019

%t a[1] = 0; a[n_] := Plus @@ (2^(#[[2]] - 1) & /@ FactorInteger[n]); Table[a[n], {n, 1, 90}]

%o (PARI) a(n)={vecsum([2^(k-1) | k<-factor(n)[,2]])} \\ _Andrew Howroyd_, Oct 29 2019

%Y Cf. A000040 (positions of 1's), A008481, A011782, A162510, A324910.

%K nonn

%O 1,4

%A _Ilya Gutkovskiy_, Oct 29 2019