%I #11 May 16 2022 10:04:13

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

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

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

%N a(n) = 1 if n has exactly one prime factor of form 4*k+1 (when counted with multiplicity) and no prime factor 4*k+3 with odd multiplicity, otherwise 0.

%H Antti Karttunen, <a href="/A353813/b353813.txt">Table of n, a(n) for n = 1..100000</a>

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

%F a(n) = [A004018(n) == 8], where [ ] is the Iverson bracket.

%F a(n) <= A353812(n), a(n) <= A353814(n).

%o (PARI) A353813(n) = { my(f = factor(n), nb1 = 0, p, ep); for(i=1, #f~, p = f[i, 1]; ep = f[i, 2]; if(1==(p%4), nb1++; if((ep>1)||(nb1>1), return(0))); if((3==(p%4)) && (ep%2), return(0))); return(1==nb1); }; \\ After "isok" function in A230779

%o (PARI)

%o A004018(n) = if(n<1, n==0, 4 * sumdiv( n, d, (d%4==1) - (d%4==3))); \\ From A004018

%o A353813(n) = (8==A004018(n));

%Y Characteristic function of A230779.

%Y Cf. A004018, A353814.

%Y Differs from A353812 for the first time at n=325, where a(325) = 0, while A353812(325) = 1.

%K nonn

%O 1

%A _Antti Karttunen_, May 14 2022