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.

A332425 If n = Product (p_j^k_j) then a(n) = Sum ((-1)^(pi(p_j) + 1) * p_j * k_j), where pi = A000720.

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%I A332425 #5 Feb 13 2020 02:54:03
%S A332425 0,2,-3,4,5,-1,-7,6,-6,7,11,1,-13,-5,2,8,17,-4,-19,9,-10,13,23,3,10,
%T A332425 -11,-9,-3,-29,4,31,10,8,19,-2,-2,-37,-17,-16,11,41,-8,-43,15,-1,25,
%U A332425 47,5,-14,12,14,-9,-53,-7,16,-1,-22,-27,59,6,-61,33,-13,12,-8,10,67,21,20
%N A332425 If n = Product (p_j^k_j) then a(n) = Sum ((-1)^(pi(p_j) + 1) * p_j * k_j), where pi = A000720.
%C A332425 Sum of prime factors of n (counted with multiplicity) with odd indices minus the sum of prime factors of n (counted with multiplicity) with even indices.
%H A332425 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%e A332425 a(252) = a(2^2 * 3^2 * 7) = a(prime(1)^2 * prime(2)^2 * prime(4)) = 2 + 2 - 3 - 3 - 7 = -9.
%t A332425 a[n_] := Plus @@ ((-1)^(PrimePi[#[[1]]] + 1) #[[1]] #[[2]] & /@ FactorInteger[n]); a[1] = 0; Table[a[n], {n, 1, 69}]
%Y A332425 Cf. A000720, A001414, A002129, A071321, A112798, A195017, A325699, A332424.
%K A332425 sign
%O A332425 1,2
%A A332425 _Ilya Gutkovskiy_, Feb 12 2020