This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A328892 #16 Oct 30 2019 20:18:08 %S A328892 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 A328892 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 A328892 2,3,1,6,1,2,3,3,2,3,1,9,8,2,1,4,2,2,2,5,1,4 %N A328892 If n = Product (p_j^k_j) then a(n) = Sum (2^(k_j - 1)). %H A328892 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a> %F A328892 If n = Product (p_j^k_j) then a(n) = Sum ordered partition(k_j). %F A328892 Additive with a(p^e) = 2^(e-1). %e A328892 a(72) = 6 because 72 = 2^3 * 3^2 and 2^(3 - 1) + 2^(2 - 1) = 6. %p A328892 a:= n-> add(2^(i[2]-1), i=ifactors(n)[2]): %p A328892 seq(a(n), n=1..100); # _Alois P. Heinz_, Oct 29 2019 %t A328892 a[1] = 0; a[n_] := Plus @@ (2^(#[[2]] - 1) & /@ FactorInteger[n]); Table[a[n], {n, 1, 90}] %o A328892 (PARI) a(n)={vecsum([2^(k-1) | k<-factor(n)[,2]])} \\ _Andrew Howroyd_, Oct 29 2019 %Y A328892 Cf. A000040 (positions of 1's), A008481, A011782, A162510, A324910. %K A328892 nonn %O A328892 1,4 %A A328892 _Ilya Gutkovskiy_, Oct 29 2019