A342025 - OEIS

%I #14 Mar 11 2021 21:07:59

%S 1,1,0,1,0,0,0,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,

%T 1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,1,0,0,0,1,0,0,0,0,

%U 0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,0,0,1,0,0,0,1,1

%N a(n) = 1 if n has the same numbers of prime factors of forms 4*k+1 and 4*k+3 when counted with multiplicity, otherwise 0.

%H Antti Karttunen, <a href="/A342025/b342025.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>

%t {1}~Join~Table[Boole[Count[#, 1] == Count[#, 3]] &@ Mod[Flatten[ConstantArray[#1, #2] & @@@ FactorInteger[n]], 4], {n, 2, 120}] (* _Michael De Vlieger_, Mar 11 2021 *)

%o (PARI) A342025(n) = {my(f = factor(n)); sum(k=1, #f~, ((f[k, 1] % 4)==1)*f[k, 2]) == sum(k=1, #f~, ((f[k, 1] % 4)==3)*f[k, 2]); }; \\ From isok function in A072202

%o (Python)

%o from sympy import factorint

%o def A342025(n):

%o     f = factorint(n)

%o     return int(sum(b for a, b in f.items() if a % 4 == 3) == sum(b for a, b in f.items() if a % 4 == 1)) # _Chai Wah Wu_, Mar 09 2021

%Y Characteristic function of A072202.

%K nonn

%O 1

%A _Antti Karttunen_, Mar 09 2021