cp's OEIS Frontend

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.

A328892 If n = Product (p_j^k_j) then a(n) = Sum (2^(k_j - 1)).

This page as a plain text file.
%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