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.

A305053 If n = Product_i prime(x_i)^k_i, then a(n) = Sum_i k_i * omega(x_i) - omega(n), where omega = A001221 is number of distinct prime factors.

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%I A305053 #12 Jun 13 2018 03:49:32
%S A305053 0,-1,0,-1,0,-1,0,-1,1,-1,0,-1,1,-1,0,-1,0,0,0,-1,0,-1,0,-1,1,0,2,-1,
%T A305053 1,-1,0,-1,0,-1,0,0,1,-1,1,-1,0,-1,1,-1,1,-1,1,-1,1,0,0,0,0,1,0,-1,0,
%U A305053 0,0,-1,1,-1,1,-1,1,-1,0,-1,0,-1,1,0,1,0,1,-1,0
%N A305053 If n = Product_i prime(x_i)^k_i, then a(n) = Sum_i k_i * omega(x_i) - omega(n), where omega = A001221 is number of distinct prime factors.
%F A305053 Totally additive with a(prime(n)) = omega(n) - 1.
%F A305053 a(n) = A305054(n) - A001221(n). - _Michel Marcus_, Jun 09 2018
%e A305053 2925 = prime(2)^2 * prime(3)^2 * prime(6)^1, so a(2925) = 2*1 + 2*1 + 1*2 - 3 = 3.
%t A305053 Table[If[n==1,0,Total@Cases[FactorInteger[n],{p_,k_}:>(k*PrimeNu[PrimePi[p]]-1)]],{n,100}]
%o A305053 (PARI) a(n) = {my(f=factor(n)); sum(k=1, #f~, f[k,2]*omega(primepi(f[k,1]))) - omega(n);} \\ _Michel Marcus_, Jun 09 2018
%Y A305053 Cf. A001221, A003963, A056239, A112798, A286520, A290103, A302242, A304714, A304716, A305052, A305054.
%K A305053 sign
%O A305053 1,27
%A A305053 _Gus Wiseman_, May 24 2018