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.

A193510 Number of even divisors of Omega(n).

This page as a plain text file.
%I A193510 #16 Jul 05 2023 17:34:06
%S A193510 0,0,0,1,0,1,0,0,1,1,0,0,0,1,1,2,0,0,0,0,1,1,0,2,1,1,0,0,0,0,0,0,1,1,
%T A193510 1,2,0,1,1,2,0,0,0,0,0,1,0,0,1,0,1,0,0,2,1,2,1,1,0,2,0,1,0,2,1,0,0,0,
%U A193510 1,0,0,0,0,1,0,0,1,0,0,0
%N A193510 Number of even divisors of Omega(n).
%C A193510 Omega(n) is the number of prime divisors of n counted with multiplicity, A001222 (also called bigomega(n)).
%C A193510 Records are at 4^A002182(n). [_Charles R Greathouse IV_, Jul 29 2011]
%H A193510 Charles R Greathouse IV, <a href="/A193510/b193510.txt">Table of n, a(n) for n = 1..10000</a>
%e A193510 a(16) = 2 because Omega(16) = 4 and the 2 even divisors are {2, 4}.
%t A193510 f[n_] := Block[{d = Divisors[PrimeOmega[n]]}, Count[EvenQ[d], True]]; Table[f[n], {n, 80}]
%t A193510 Join[{0},Table[Count[Divisors[PrimeOmega[n]],_?EvenQ],{n,2,100}]] (* _Harvey P. Dale_, Jul 05 2023 *)
%o A193510 (PARI) a(n)=my(k=bigomega(n));if(!k||k%2,0,numdiv(k/2)) \\ _Charles R Greathouse IV_, Jul 29 2011
%Y A193510 Cf. A183063, A001222, A193509.
%K A193510 nonn
%O A193510 1,16
%A A193510 _Michel Lagneau_, Jul 29 2011